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LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA 


OF" 


Class 


l'l{eolff|i«al 


Presented  by 


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OF  THE 

UNIVERSITY 

OF 

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Telescopic  view  of  the  Moon. 


Telescopic  view  of  the  Moon  when  five  days  old. 


COMPENDIUM  OF  ASTRONOMY; 

CONTAINING  THE 

ELEMENTS    OF    THE    SCIENCE, 

FAMILIARLY   EXPLAINED  AND  ILLUSTRATED, 

WITH    THE    LATEST    DISCOVERIES. 

N. 

ADAPTED  TO  THE  USE   OF 

SCHOOLS   AND   ACADEMIES, 

AND  OF   THB 

GENERAL    READER. 

STEREOTYPE    EDITION. 

BY  DENISON  OLMSTED,  A.  M. 

PROFESSOR  OP  NATURAL  PHILOSOPHY  AND  ASTRONOMY  IN  YALE  COLLEGE. 


NEW  YORK: 
ROBERT     B.     COLLINS 

254    PEARL    STREET. 
,     1852. 

inr? 

OF  THE 

UNIVERSITY 


Entered  according  to  Act  of  Congress,  in  the  year  1839,  by 


DENISON  OLMSTED 


in  the  Clerk's  office,  of  the  District  Court  of  Connecticut. 


PREFACE. 


THIS  small  volume  is  intended  to  afford  to  the  General 
Reader,  and  to  the  more  advanced  pupils  of  our  Schools  and 
Academies,  a  comprehensive  outline  of  Astronomy  with  its 
latest  discoveries.  For  its  perusal,  no  further  acquaintance 
with  mathematics  is  necessary,  than  a  knowledge  of  common 
arithmetic ;  although  some  slight  knowledge,  at  least,  of  ge- 
ometry an4  trigonometry  will  prove  very  useful. 

By  omitting  mathematical  formulae,  and  employing  much 
familiar  illustration,  we  have  endeavored  to  bring  the  leading 
facts  and  doctrines  of  this  noble  and  interesting  science,  within 
the  comprehension  of  every  attentive  and  intelligent  reader. 
In  no  science,  more  than  in  this,  are  greater  advantages  to  be 
derived  from  a  lucid  arrangement — an  order  which  brings  out 
every  fact  and  doctrine  of  the  science,  just  in  the  place  where 
the  mind  is  ready  to  receive  it.  A  certain  maturity  of  mind, 
and  power  of  reflection,  are,  however,  indispensable  for  under- 
standing this  science.  Astronomy  is  no  study  for  children. 
Let  them  be  employed  on  subjects  more  suited  to  the  state  of. 
their  capacities,  until  those  faculties  are  more  fully  developed, 
which  will  enable  them  to  learn  to  conceive  correctly  of  the 
celestial  motions.  A  work  on  Astronomy  that  is  very  easy, 
must  be  very  superficial,  and  will  be  found  to  enter  little  into 
the  arcana  of  the  science.  The  riches  of  this  mine  lie  deep  ; 
and  no  one  can  acquire  them,  who  is  either  incompetent  or 
unwilling  to  penetrate  beneath  the  surface. 

Although  -this  treatise  is  based  on  the  larger  work  of  the 
author,  ("  Introduction  to  Astronomy,")  prepared  for  the  stu- 
dents of  Yale  College,  yet  it  is  not  merely  an  abridgment  of 
that.  It  contains  much  original  matter  adapted  to  the  pecu- 
liar exigencies  of  the  class  of  readers  for  whom  it  is  intended. 
The  few  passages  taken  verbatim  from  astronomical  writers, 


O  f\  f\ 


IV  PREFACE. 

are  not,  as  in  the  larger  work,  always  accredited  to  their  re- 
spective  authors,  as  this  was  deemed  unimportant  in  a  work 
of  this  description. 

It  is  strongly  recommended  to  all  who  study  this  science, 
even  in  its  most  elementary  form,  early  to  commence  learning 
the  names  of  the  constellations,  and  of  the  largest  of  the  in- 
dividual stars,  in  the  order  in  which  they  are  described  in  the 
last  part  of  the  work.  A  celestial  globe  will  be  found  a  most 
useful  auxiliary  in  this  as  in  every  other  part  of  Astronomy. 
If  it  cannot  supersede,  it  may  greatly  aid  reflection.  The 
reader  also  should,  if  in  his  power,  take  frequent  opportunities 
of  viewing  the  heavenly  bodies  through  the  telescope.  This 
will  add  much  to  his  intelligence,  and  increase  his  interest  in 
the  study. 


ADVERTISEMENT. 

SINCE  the  stereotype  edition  of  this  work  was  first  pub- 
lished, several  new  and  interesting  discoveries  have  been  added 
to  Astronomy,  an  account  of  which  will  be  found  in  the  Sup- 
plement. They  make  no  change  in  the  great  facts  and  doc- 
trines of  the  science,  but  these  remain  unaltered  and  immu- 
table ;  while  the  new  discoveries  extend  still  further  our 
knowledge  of  the  Universe.  We  have,  therefore,  no  occasion 
to  alter  the  text,  except  perhaps  very  slightly  in  one  or  two 
statements,  but  by  giving  whatever  is  new  and  important  in 
the  form  of  a  supplement,  (to  which  we  may  add  as  every 
successive  discovery  is  made,)  we  shall  endeavor  to  secure  to 
this  treatise  the  freshness  and  accuracy  of  the  most  recent 
compilations,  as  well  as  furnish  to  the  schools  what  has  been 
thoroughly  tested  and  approved  by  the  most  able  teachers  of 
the  Union. 


CONTENTS. 

Preliminary  Observations,  -        -  Page 

Part  I.     OF  THE  EARTH. 

Chapter  I. — Of  the  Figure  and  Dimensions  of  the  Earth, 

and  the  Doctrine  of  the  Sphere,  ...  5 
Chapter  II. — Of  the  Diurnal  Revolution — Artificial 

Globes,     -  i^l 

Chapter  III.— Of  Parallax,  Refraction,  and  Twilight,  36 
Chapter  IV.— Of  Time,  -  -  45 

Chapter    V. — Of    Astronomical    Instruments — Figure 

and  Density  of  the  Earth,  -       51 

Part  II.    OF  THE  SOLAR  SYSTEM. 

Chapter  I. — Of  the  Sun — Solar  Spots — Zodiacal  Light,  70 
Chapter  II.  Of  the  Apparent  Annual  Motion  of  the 

Sun— Seasons — Figure  of  the  Earth's  Orbit,  -  79 
Chapter  III. — Of  Universal  Gravitation — Kepler's 

Laws, — Motion  in  an  Elliptical  Orbit — Precession 

of  the  Equinoxes,  -  -  91 

Chapter  IV. — Of  the  Moon — Phases,  Revolutions,  -  110 
Chapter  V.— Of  Eclipses,  -  -  137 

Chapter  VI.— Of  Longitude — Tides,  -  150 

Chapter  VII. — Of  the  Planets— the  Inferior  Planets, 

Mercury  and  Venus,  -  1 67 

Chapter  VIII. — Of  the  Superior  Planets — Mars,  Jupiter, 

Saturn  and  Uranus — Ceres,  Pallas,  Juno  and  Vesta,     183 


Vl  OONTBNT8. 

Page 

Chapter  IX. — Of  the  Motions  of  the  Planetary  System 
— Quantity  of  Matter  in  the  Sun  and  Planets — 
Stability  of  the  Solar  System,  -  -  205 

Chapter  X.— Of  Comets,  -        -        -    218 

Part  III.     OF  THE  FIXED  STARS  AND  THE  SYS- 
TEM  OF  THE  WORLD. 

Chapter  I.— Of  the  Fixed  Stars  Constellations,  -  235 

Chapter  II.— Of  Clusters  of  Stars — Nebulae — Variable 

Stars — Temporary  Stars — Double  Stars,  -  -  247 

Chapter  III.— Of  the  Motions  of  the  Fixed  Stars— Dis- 
tances— Nature,  -  ...  -  255 

Chapter  IV.— Of  the  System  of  the  World,        -         -  265 


COMPENDIUM  OF  ASTRONOMY, 


PRELIMINARY  OBSERVATIONS. 

1.  ASTRONOMY  is  that  science  which  treats  of  the  heav- 
enly bodies. 

More  particularly,  its  object  is  to  teach  what  is  known 
respecting  the  Sun,  Moon,  Planets,  Comets,  and  Fixed 
Stars ;  and  also  to  explain  the  methods  by  which  this 
knowledge  is  acquired. 

Astronomy  is  sometimes  divided  into  Descriptive, 
Physical,  and  Practical.  Descriptive  Astronomy  re- 
spects  facts ;  Physical  Astronomy,  causes  ;  Practical  As- 
tronomy, the  means  of  investigating  the  facts,  whether 
by  instruments,  or  by  calculation.  It  is  the  province  of 
Descriptive  Astronomy  to  observe,  classify,  and  record, 
all  the  phenomena  of  the  heavenly  bodies,  whether  per- 
taining to  those  bodies  individually,  or  resulting  from 
their  motions  and  mutual  relations.  It  is  the  part  of 
Physical  Astronomy  to  explain  the  causes  of  these  phe- 
nomena by  investigating  and  applying  the  general  laws 
on  which  they  depend ;  especially  by  tracing  out  all  the 
consequences  of  the  law  of  universal  gravitation.  Prac- 
tical Astronomy  lends  its  aid  to  both  the  other  depart- 
ments. 

2.  Astronomy  is  the  most  ancient  of  all  the  sciences. 
At  a  period  of  very  high  antiquity,  it  was  cultivated  in 
Egypt,  in  Chaldea,  and  in  India.     Such  knowledge  of 
the  heavenly  bodies  as  could  be  acquired  by  close  and 
long  continued  observation,  without  the  aid  of  instru- 


1  -  Define  Astronomy.  What  does  it  teach  ?  Name  the  three 
parta  into  which  it  is  divided.  What  does  Descriptive  Astron- 
omy respect  ?  What  does  Physical  Astronomy  ?  What  does 
Practical  Astronomy  ?  What  is  the  peculiar  province  of  each  ? 


2  PRELIMINARY  OBSERVATIONS. 

ments,  was  diligently  amassed ;  and  tables  of  the  celes- 
tial motions  were  constructed,  which  could  be  used  in 
predicting  eclipses,  and  other  astronomical  phenomena. 

About  500  years  before  the  Christain  era,  Pythago- 
ras, of  Greece,  taught  astronomy  at  the  celebrated  school 
at  Crotona,  (a  Greek  town  on  the  southeastern  coast  of 
Italy,)  and  exhibited  more  correct  views  of  the  nature 
of  the  celestial  motions,  than  were  entertained  by  any 
other  astronomer  of  the  ancient  world.  His  views,  how- 
ever, were  not  generally  adopted,  but  lay  neglected  for 
nearly  2000  years,  when  they  were  revived  and  estab- 
lished by  Copernicus  and  Galileo.  The  most  celebrated 
astronomical  school  of  antiquity,  was  at  Alexandria  in 
Egypt,  which  was  established  and  sustained  by  the  Ptol- 
emies, (Egyptian  princes,)  300  years  before  the  Chris- 
tian era.  The  employment  of  instruments  for  measur- 
ing angles,  and  bringing  in  trigonometrical  calculations 
to  aid  the  naked  powers  of  observation,  gave  to  the  Alex- 
andrian astronomers  great  advantages  over  all  their  pre- 
decessors. 

The  most  able  astronomer  of  the  Alexandrian  school 
was  Hipparchus,  who  was  distinguished  above  all  the 
ancients  for  the  accuracy  of  his  astronomical  measure- 
ments and  determinations.  The  knowledge  of  astron- 
omy possessed  by  the  Alexandrian  school,  and  recorded 
in  the  Almagest,  or  great  work  of  Ptolemy,  constituted 
the  chief  of  what  was  known  of  our  science  during  the 
middle  ages,  until  the  fifteenth  and  sixteenth  centuries, 
when  the  labors  of  Copernicus  of  Prussia,  Tycho  Brake 


2.  Trace  the  history  of  Astronomy.  Among  what  ancient 
nations  was  it  cultivated  ?  What  kind  of  knowledge  of  the 
heavenly  bodies  was  amassed  ?  Who  was  Pythagoras?  When 
and  where  did  he  live  ?  Where  was  his  school  ?  How  correct 
were  his  views  ?  Were  they  generally  adopted  ?  Give  an  ac- 
count of  the  Alexandrian  school.  When  was  it  established  and 
by  whom  ?  What  gave  it  great  advantages  over  all  its  prede- 
cessors ?  Give  some  account  of  Hipparchus — of  Ptolemy — of 
Copernicus — of  Tycho  Brahe — of  Kepler — of  Galileo — of 
Newton — of  La  Place.  Specify  the  respective  labors  of  each 


PRELIMINARY  OBSERVATIONS. 


of  Denmark,  Kepler  of  Germany,  and  Galileo  of  Italy, 
laid  the  solid  foundations  of  modern  astronomy.  Coper- 
nicus expounded  the  true  system  of  the  world,  or  the 
arrangement  and  motions  of  the  heavenly  bodies ;  Ty- 
cho  Brahe  carried  the  use  of  instruments,  and  the  art  of 
astronomical  observation,  to  a  far  higher  degree  of  accu- 
racy than  had  ever  been  done  before  ;  Kepler  discovered 
the  great  laws  which  regulate  the  movements  of  the 
planets ;  and  Galileo,  having  first  enjoyed  the  aid  of  the 
telescope,  made  innumerable  discoveries  in  the  solar 
system.  Near  the  beginning  of  the  eighteenth  century, 
Sir  Isaac  Newton  discovered,  in  the  law  of  universal 
gravitation,  tho  great  principle  mat  explains  the  causes 
of  all  celestial  phenomena ;  and  recently,  La  Place  has 
more  fully  completed  what  Newton  begun,  having  fol- 
lowed out  all  the  consequences  of  the  law  of  universal 
gravitation,  in  his  great  work,  the  Mecanique  Celeste. 

3.  Among  the  ancients,  astronomy  was  studied  chiefly 
as  subsidiary  to  astrology.     Astrology  was  the  art  of  di- 
vining future  events  by  the  stars.     It  was  of  two  kinds, 
natural  and  judicial.     Natural  Astrology,  aimed  at  pre- 
dicting remarkable  occurrences  in  the  natural  world,  as 
eathquakes,   volcanoes,   tempests,   and  pestilential  dis- 
eases.    Judicial  Astrology,  aimed  at  foretelling  the  fates 
of  individuals,  or  of  empires. 

4.  Astronomers  of  every  age,  have  been  distinguished 
for  their  persevering  industry,  and  their  great  love  of  ac- 
curacy.    They  have  uniformly  aspired  to  an  exactness 
in  their  inquiries,  far  beyond  what  is  aimed  at  in  most 
geographical  investigations,  satisfied  with  nothing  short 
of  numerical  accuracy  wherever  this  is  attainable  ;  and 
years  of  toilsome  observation,  or  laborious  calculation, 
have  been  spent  with  the  hope  of  attaining  a  few  se- 


3.  Define  Astrology.     What  was  Natural  and  what  Judicial 
Astrology  ? 

4.  What  is  said  of  the  industry  and  accuracy  of  astrono- 
mers  ?     Can  this  science  be  taught  by  artificial  aids  alone  ? 


4  PRELIMINARY  OBSERVATIONS. 

conds  nearer  to  the  truth.  Moreover,  a  severe  but  de 
lightful  labor  is  imposed  on  all,  who  would  arrive  at  a 
clear  and  satisfactory  knowledge  of  the  subject  of  astron- 
omy. Diagrams,  artificial  globes,  orreries,  and  familiar 
comparisons  and  illustrations,  proposed  by  the  author  or 
the  instructor,  may  afford  essential  aid  to  the  learner, 
but  nothing  can  convey  to  him  a  perfect  comprehension 
of  the  celestial  motions,  without  much  diligent  study 
and  reflection. 

5.  In  this  treatise,  we  shall  for  the  present  assume  the 
Copernican  system  as  the  true  system  of  the  world, 
postponing  the  discussion  of  the  evidence  on  which  it 
rests  to  a  late  period,  when  the  learner  has  been  made  ex- 
tensively acquainted  with  astronomical  facts.  This  sys- 
tem maintains  (1,)  That,  the  apparent  diurnal  revolution 
of  the  heavenly  bodies,  from  east  to  west,  is  owing  to 
the  real  revolution  of  the  earth  dn  its  own  axis  from 
west  to  east,  in  the  same  time ;  and  (2,)  That  the  sun 
is  the  center  around  which  the  earth  and  planets  all  re- 
volve from  west  to  east,  contrary  to  the  opinion  that  the 
earth  is  the  center  of  motion  of  the  sun  and  planets. 


5.  What  system  is  assumed  as  the  true  system  of  the  world  ? 
Specify  the  two  leading  points  in  the  Copernican  system. , 


PART  I. OF  THE  EARTH. 


CHAPTER   I. 

OF  THE  FIGURE  AND  DIMENSIONS  OF  THE  EARTH,  AND  THE 
DOCTRINE  OF  THE  SPHERE. 

6.  The  figure  of  the  earth  is  nearly  globular.  This 
fact  is  known,  first,  by  the  circular  form  of  its  shadow 
cast  upon  the  moon  in  a  lunar  eclipse  ;  secondly,  from 
analogy,  each  of  the  other  planets  being  seen  to  be 
spherical ;  thirdly,  by  our  seeing  the  tops  of  distant  ob- 
jects while  the  other  parts  are  invisible,  as  the  topmast 
of  a  ship,  while  either  leaving  or  approaching  the  shore, 
or  the  lantern  of  a  light-house,  which  when  first  descried 
at  a  distance  at  sea,  appears  to  glimmer  upon  the  very 
surface  of  the  water ;  fourthly,  by  the  testimony  of  nav- 
igators who  have  sailed  around  it ;  and,  finally,  by  ac- 
tual observations  and  measurements,  made  for  the  ex- 
press purpose  of  ascertaining  the  figure  of  the  earth,  by 
means  of  which  astronomers  are  enabled  to  compute  the 
distances  from  the  center  of  the  earth  of  various  places 
on  its  surface,  which  distances  are  found  to  be  nearly 
equal. 

The  effect  of  the  rotundity  of  the  earth  upon  the  ap- 
pearance of  a  ship,  when  either  leaving  or  approaching 
the  spectator,  is  illustrated  by  Fig.  1. 

As  light  proceeds  in  straight  lines,  it  is  evident  that, 
if  the  earth  is  round,  the  top  of  the  ship  ought  to  come 
into  view  before  the  lower  parts,  when  the  ship  is  ap- 
proaching the  spectator  at  A,  and  to  remain  longest  iii 
view  when  the  ship  is  leaving^him.  But,  were  the  eartL 


6.  What  is  the  figure  of  the  earth"?    Enumerate  the  various 
proofs  of  its  rotundity. 


a  continued  plane,  then  the  spectator  would  see  all  parts 
of  the  ship  at  the  same  time,  as  is  represented  in  the  an- 
nexed figure. 

Fig.  2. 


7.  The  foregoing  considerations  show  that  the  form 
of  the  earth  is  spherical ;  but  more  exact  determinations 
prove,  that  the  earth,  though  nearly  globular,  is  not  ex- 
actly so ;  its  diameter  from  the  north  to  the  south  pole 
is  about  26  miles  less  than  through  the  equator,  giving 
to  the  earth  the  form  of  an  oblate  spheroid,  or  a  flattened 
sphere  resembling  an  orange.  We  shall  reserve  the  ex- 


FIGURE  AND  DIMENSIONS.      ;  7 

planations  of  the  methods  by  which  this  fact  is  estab- 
lished, until  the  learner  is  better  prepared  than  at  present 
to  understand  them. 

The  mean  or  average  diameter  of  the  earth,  is  7912.4 
miles,  a  measure  which  the  learner  should  fix  in  his 
memory  as  a  standard  of  comparison  in  astronomy,  and 
of  which  he  shoulc1  endeavor  to  form  the  most  adequate 
conception  in  his  power.  The  circumference  of  the 
earth  is  about  25,000  miles.  Although  the  surface  of 
the  earth  is  uneven,  sometimes  rising  in  high  mountains, 
and  sometimes  descending  in  deep  valleys,  yet  these  ele- 
vations and  depressions  are  so  small  in  comparison  with 
the  immense  volume  of  the  globe,  as  hardly  to  occasion 
any  sensible  deviation  from  a  surface  uniformly  curvi- 
linear. The  irregularities  of  the  earth's  surface,  in  this 
view,  are  no  greater  than  the  rough  points  on  the  rind 
of  an  orange,  which  do  not  perceptibly  interrupt  its  con- 
tinuity ;  for  the  highest  mountain  on  the  globe  is  only 
about  five  miles  above  the  general  level  ;  and  the  deep- 
est mine  hitherto  opened  is  only  about  half  a  mile.* 

~  T~W  or  a^out  one  sixteen  hundredth  part 


of  the  whole  diameter,  an  inequality  which,  in  an  arti- 
ficial globe  of  eighteen  inches  diameter,  amounts  to  only 
the  eighty  eighth  part  of  an  inch. 

8.  The  greatest  difficulty  in  the  way  of  acquiring 
correct  views  in  astronomy,  arises  from  the  erroneous 
notions  that  pre-occuoy  the  mind.  To  divest  himself 


7.  What  is  the  exact  figure  of  the  earth  ?  How  much  greater 
is  its  diameter  through  the  equator  than  through  the  poles  ?, 
What  is  the  mean  average  diameter  of  the  earth  ?  What  is  its 
circumference  1  Do  the  inequalities  on  the  earth's  surface  af- 
fect its  rotundity  ?  To  what  may  these  be  compared  ?  How 
high  is  the  highest  mountain  above  the  general  level  ?  How 
deep  is  the  deepest  mine  ?  To  how  much  would  this  amount 
on  an  artificial  globe  eighteen  inches  in  diameter  ? 

*  Sir  John  Herschel. 


8  THE  EARTH. 

of  these,  the  learner  should  conceive  of  the  earth  as  a 
huge  globe  occupying  a  small  portion  of  space,  and  en- 
circled on  all  sides  with  the  starry  sphere.  He  should 
free  his  mind  from  its  habitual  proneness  to  consider  one 
part  of  space  as  naturally  up  and  another  down,  and 
view  himself  as  subject  to  a  force  which  binds  him  to 
the  earth  as  truly  as  though  he  were  fastened  to  it  by 
some  invisible  cords  or  wires,  as  the  needle  attaches  it- 
self to  all  sides  of  a  spherical  loadstone.  He  should 

Fig.  3. 


dwell  on  this  point  until  it  appears  to  him  as  truly  up  in 
the  direction  of  BB,  CC,  DD,  (Fig.  3,)  when  he  is  at 
B,  C,  and  D,  respectively,  as  in  the  direction  *AA,  when 
he  is  at  A. 


DOCTRINE  OF  THE  SPHERE. 


9.  The  definitions  of  the  different  lines,  points,  and 
circles,  which  are  used  in  astronomy,  and  the  proposi- 
tions founded  upon  them,  compose  the  Doctrine  of  the 
Sphere. 


8.  Whence  arises  the  greatest  difficulty  in  acquiring  correct 
views  in  astronomy  ?     How  should  the  learner  conceive  of 
the  earth  ?     Illustrate  by  figure  3. 

9.  Doctrine  of  the  sphere — define  it. 


DOCTRINE  OF  THE  SPHERE.  9 

10.  A  section  of  a  sphere  by  a  plane  cutting  it  in  any 
manner,  is  a  circle.  Great  circles  are  those  which  pass 
through  the  center  of  the  sphere,  and  divide  it  into  two 
equal  hemispheres  :  Small  circles,  are  such  as  do  not 
pass  through  the  center,  but  divide  the  sphere  into  two 
unequal  parts.  Every  circle,  whether  great  or  small,  is 
divided  into  360  equal  parts  called  degrees.  A  degree, 
therefore,  is  not  any  fixed  or  definite  quantity,  but  only 
a  certain  aliquot  part  of  any  circle.* 

The  axis  of  a  circle,  is  a  straight  line  passing  through 
its  center  at  right  angles  to  its  plane. 


Fig.  4. 


*  As  this  work  may  be  read  by  some  who  are  unacquainted  with 
even  the  rudiments  of  geometry,  we  annex  a  few  particulars  respecting 
angular  measurements. 

A  line  drawn  from  the  center  to  the  circumference  of  a  circle  is 
called  a  radius,  as  CD,  fig.  4. 

Any  part  of  the  circumference  of  a  circle  is  called  an  arc,  as  AB, 
or  BD. 

An  angle  'is  measured  by  the 
arc  included  between  two  radii. 
Thus,  in  the  annexed  figure,  the 
angle  contained  between  the  two 
radii  CA  and  CB,  that  is,  the  an- 
gle ACB,  is  measured  by  the  arc 
AB.  But  this  arc  is  the  same  part 
of  the  smaller  circle  that  EF  is  of 
the  greater.  The  arc  AB  there- 
fore contains  the  same  number  of 
degrees  as  the  arc  EF,  and  either 
may  be  taken  for  the  measure  of- 
the  angle  ACB.  As  the  whole 
circle  contains  360°,  it  is  evident 
that  the  quarter  of  a  circle,  or'quad- 


rant  ABD,  contains  90°,  and  the 
semicircle  ABDG  contains  180°. 
r  The  complement  of  an  arc  or  an- 
gle,^ what  it  wants  of  90°.  Thus  BD  is  the  complement  of  AB,  and 
AB  is  the  complement  of  BD.  If  AB  denotes  a  certain  number  of  de- 
grees of  latitude,  BD  will  be  the  complement  of  the  latitude  or  the  co- 
latitude,  as  it  is  commonly  written. 

The  supplement  of  an  arc  or  angle,  is  what  it  wants  of  180°. 
Thus  BA  is  the  supplement  of  GDB,  and  GDB,  is  the  supplement 
of  BA.  If  BA  were  20°  of  longitude,  GDB  its  supplement  would 
be  160°. 

An  angle  is  said  to  be  subtended  by  the  side  which  is  opposite  to  it. 
Thus  in  the  triangle  ACK,  the  angle  at  C  is  subtended  by  the  side  AK, 
the  angle  at  A  by  CK,  and  the  angle  at  K  by  CA.  In  like  manner  a 
side  is  said  to  be  subtended  by  an  angle,  as  AK  by  the  angle  at  C. 


10 


THE  EARTH. 


The  pole  of  a  great  circle,  is  the  point  on  the  sphere 
where  its  axis  cuts  through  the  sphere.  Every  great 
circle  has  two  poles,  each  of  which  is  every  where  90° 
from  the  great  circle. 

All  great  circles  of  the  sphere  cut  each  other  in  two 
points  diametrically  opposite,  and  consequently,  their 
points  of  section  are  180°  apart. 

A  great  circle  which  passes  through  the  pole  of  an- 
other great  circle,  cuts  the  latter  at  right  angles. 

The  great  circle  which  passes  through  the  pole  of  an- 
other great  circle  and  is  at  right  angles  to  it,  is  called  a 
secondary  to  that  circle. 

The  angle  made  by  two  great  circles  on  the  surface 
of  the  sphere,  is  measured  by  the  arc  of  another  great 
circle,  of  which  the  angular  point  is  the  pole,  being  the 
arc  of  that  great  circle  intercepted  between  those  two 
circles. 

11.  In  order  to  fix  the  position  of  any  plane,  either  on 
the  surface  of  the  earth  or  in  the  heavens,  both  the  earth 
and  the  heavens  are  conceived  to  be  divided  into  sepa- 
rate portions  by  circles,  which  are  imagined  to  cut 
through  them  in  various  ways.  The  earth  thus  inter- 
sected is  called  the  terrestrial,  and  the  heavens  the  ce- 
lestial sphere.  The  learner  will  remark,  that  these  cir- 
cles have  no  existence  in  nature,  but  are  mere  land- 
marks, artificially  contrived  for  convenience  of  refer- 


10.  What  figure  is  produced  by  the  section  of  a  sphere? 
Define  great  circles.     Define  small  circles.     Into  how  many 
degrees  is  every  circle  divided  ?  Is  a  degree  any  fixed  or  defi- 
nite quantity  ?    What  is  the  axis  of  a  circle  ?     What  is  the  pole 
of  a  circle?     How  do  all  great  circles  cut  each  other?     How 
is  a  great  circle  cut  by  another  great  circle  passing  through  its 
pole  ?    What  is  the  secondary  of  a  circle  ?    How  is  the  angle 
made  by  two  great  circles  on  the  surface  of  the  sphere  measured? 

11.  How  are  the  earth  and  the  heavens  conceived  to  be  di- 
vided ?     What  constitutes  the  terrestrial  sphere  ?     What  the 
celestial  ?     Have  these  circles  any  existence  in  nature  ?     In 
what  do  the  heavenly  bodies  appear  to  be  fixed  ? 


DOCTRINE  OF  THE  SPHERE.  11 

ence.  On  account  of  the  immense  distance  of  the  heav- 
enly bodies,  they  appear  to  us,  wherever  we  are  placed, 
to  be  fixed  in  the  same  concave  surface,  or  celestial 
vault.  The  great  circles  of  the  globe,  extended  every 
way  to  meet  the  concave  surface  of  the  heavens,  become 
circles  of  the  celestial  sphere. 

12.  The  Horizon  is  the  great  circle  which  divides 
the  earth  into  upper  and  lower  hemispheres,  and  sepa- 
rates the  visible  heavens  from  the  invisible.     This  is 
the  rational  horizon.     The  sensible  horizon,  is  a  circle 
touching  the  earth  at  the  place  of  the  spectator,  and  is 
bounded  by  the  line  in  which  the  earth  and  skies  seem 
to  meet.     The  sensible  horizon  is  parallel  to  the  ra- 
tional, but  is  distant  from  it  by  the  semi-diameter  of  the 
earth,  or  nearly  4,000  miles.     Still,  so  vast  is  the  dis- 
tance of  the  starry  sphere,  that  both  these  planes  appear 
to  cut  that  sphere  in  the  same  line ;  so  that  we  see  the 
same  hemisphere  of  stars  that  we  should  see  if  the  up- 
per half  of  the  earth  were  removed,  and  we  stood  on  the 
rational  horizon. 

13.  The  poles  of  the  horizon  are  the  zenith  and  na- 
dir.    The  Zenith  is  the  point  directly  over  bur  head, 
and  the  Nadir  that  directly  under  our  feet.     The  plumb 
line  is  in  the  axis  of  the  horizon,  and  consequently  di- 
rected towards  its  poles. 

Every  place  on  the  surface  of  the  earth  has  its  own 
horizon ;  and  the  traveller  has  a  new  horizon  at  every 
step,  always  extending  90  degrees  from  him  in  all  di- 
rections. 


12.  Define  the  horizon.     Distinguish  between  the  rational 
and  the  sensible  horizon.     What  is  the  distance  between  the 
sensible  and  rational  horizons  ?     How  do  both  appear  to  cut 
the  starry  heavens  ? 

13.  What  are  the  poles  of  the  horizon  ?     Define  the  zenith. 
Define  the  nadir.     How  is  the  plumb  line  situated  with  respect 
*o  the  horizon?    How  manv  horizons  are  there  on  the  earth  1 


12  THE  EARTH. 

14.  Vertical  circles  are  those  which  pass  through  the 
ooles  of  the  horizon,  perpendicular  to  it. 

The  Meridian  is  that  vertical  circle  which  passes 
through  the  north  and  south  points. 

The  Prime  Vertical,  is  that  vertical  circle  which 
passes  through  the  east  and  west  points. 

The  Altitude  of  a  body,  is  its  elevation  above  the  ho- 
rizon, measured  on  a  vertical  circle. 

The  Azimuth  of  a  body,  is  its  distance  measured  on 
the  horizon  from  the  meridian  to  a  vertical  circle  passing 
through  the  body. 

'The  Amplitude  of  a  body,  is  its  distance  on  the  hori- 
zon, from  the  prime  vertical,  to  a  vertical  circle  passing 
through  the  body. 

Azimuth  is  reckoned  90°  from  either  the  north  or 
south  point ;  and  amplitude  90°  from  either  the  east  or 
west  point.  Azimuth  and  amplitude  are  mutually  com- 
plements of  each  other.  When  a  point  is  on  the  hori- 
zon, it  is  only  necessary  to  count  the  'number  of  degrees 
of  the  horizon  between  that  point  and  the  meridian,  in 
order  to  find  its  azimuth ;  but  if  the  point  is  above  the 
horizon,  then  its  azimuth  is  estimated  by  passing  a  ver- 
tical circle  through  it,  and  reckoning  the  azimuth  from 
the  point  where  this  circle  cuts  the  horizon. 

The  Zenith  Distance  of  a  body  is  measured  on  a  ver- 
tical circle,  passing  through  that  body.  It  is  the  com- 
plement of  the  altitude. 

1 5.  The  Axis  of  the  Earth  is  the  diameter,  on  which 
the  earth  is  conceived  to  turn  in  its  diurnal  revolution. 
The  same  line  continued  until  it  meets  the  starry  con- 
cave, constitutes  the  axis  of  the  celestial  sphere. 


14.  Define  vertical  circles — the  meridian — tlie  prime  verti- 
cal— altitude — azimuth — amplitude.     How   many   degrees  of 
azimuth  are  reckoned  ?  from  what  points  ?     How  are  azimuth 
and  amplitude  related  to  each  other  ?    Define  zenith  distance 
— How  is  it  related  to  the  altitude  ? 

15.  Define  the  axis  of  the  earth — the  axis  of  the  celestial 
sphere — the  poles  of  the  earth — the  poles  of  the  heavens. 


DOCTRINE   OF  THE  SPHERE.  13 

The  Poles  of  the  Earth  are  the  extremities  of  the 
earth's  axis :  the  Poles  of  the  Heavens,  the  extremities 
of  the  celestial  axis. 

16.  The  Equator  is  a  great  circle  cutting  the  axis  of 
the  earth  at  right  angles.     Hence  the  axis  of  the  earth 
is  the  axis  of  the  equator,  and  its  poles  are  the  poles  of 
the  equator.     The  intersection  of  the  plane  of  the  equa- 
tor with  the  surface  of  the  earth,  constitutes  the  terres- 
trial, and  with  the  concave  sphere  of  the  heavens,  the 
celestial  equator.     The  latter,  by  way  of  distinction,  is 
sometimes  denominated  the  equinoctial. 

17.  The  secondaries  to  the  equator,  that  is,  the  great 
circles  passing  through  the  poles  of  the  equator,  are 
called  Meridians,  because  that  secondary  which  passes 
through  the  zenith  of  any  place  is  the  meridian  of  that 
place,  and  is  at  right  angles  both  to  the  equator  and  the 
^orizon,  passing  as  it  does  through  the  poles  of  both. 
These  secondaries  are  also  called  Hour  Circles,  because 
the  arcs  of  the  equator  intercepted  between  them  are 
used  as  measures  of  time. 

18.  The  Latitude  of  a  place  on  the  earth,  is  its  dis- 
tance from  the  equator  north  or  south.     The  Polar  Dis- 
tance, or  angular  distance  from  the  nearest  pole,  is  the 
complement  of  the  latitude. 

19.  The   Longitude  of  a  place  is  its  distance  from 
some  standard  meridian,  either  east  or  west,  measured 
on  the  equator.     The  meridian  usually   taken  as   the 
standard,  is  that  of  the  Observatory  of  Greenwich,  in 
London.     If  a  place  is  directly  on  the  equator,  we  have 
only  to  inquire  how  many  degrees  of  the  equator  there 


16.  Define  the  equator.  What  constitutes  the  terrestrial 
equator  ?  what  the  celestial  equator  ?  What  is  this  also  called? 
.  17.  What  are  the  secondaries  of  the  equator  called7 

18.  Define  the  Latitude  of  a  place— the  polar  distance. 
2 


14  THE  EARTH. 

are  between  that  place  and  the  point  where  the  meridian 
of  Greenwich  cuts  the  equator.  If  the  place  is  north  or 
south  of  the  equator,  then  its  longitude  is  the  arc  of  the 
equator  intercepted  between  the  meridian  which  passes 
through  the  place,  and  the  meridian  of  Greenwich. 

20.  The  Ecliptic  is  a  great  circle  in  which  the  earth 
performs  its  annual  revolution  around  the  sun.     It  passes 
through  the  center  of  the  earth  and  the  center  of  the 
sun.     It  is  found  by  observation  that  the  earth  does  not 
lie  with  its  axis  at  right  angles  to  the  plane  of  the  eclip- 
tic, but  that  it  is  turned  about  23J  degrees  out  of  a  per- 
pendicular direction,  making  an  angle  with  the  plane 
itself  of  66i°.     The  equator,  therefore,  must  be  turned 
the  same  distance  out  of  a  coincidence  with  the  ecliptic, 
the  two  circles  making  an  angle  with  each  other  of  23J°. 
It  is  particularly  important  for  the  learner  to  form  cor- 
rect ideas  of  the  ecliptic,  and  of  its  relations  to  the  equa- 
tor, since  to  these  two  circles  a  great  number  of  astro- 
nomical measurements  and  phenomena  are  referred. 

21.  The  Equinoctial  Points,  or  Equinoxes*  are  the 
intersections  of  the  ecliptic  and  equator.     The  time 
when  the  sun  crosses  the  equator  in  going  northward 
is  called  the  vernal,  and  in  returning  southward,  the  au- 
tumnal equinox.      The    vernal    equinox   occurs    about 
the  21st  of  March,  and  the  autumnal  the  22d  of  Sep- 
tember. 


19.  Define  the  Longitude  of  a  place.     What  is  the  standard 
meridian  ?     When  a  place  is  on  the  equator,  how  is  its  longi- 
tude measured  ?  how  when  it  is  north  or  south  of  the  equator  ? 

20.  Define  the  ecliptic.     How  does  it  pass  with  respect  to 
the  earth  and  the  sun  ?    How  is  it  situated  with  respect  to  the 
equator  ? 

21.  Define  the  equinoctial  points.   When  is  the  vernal  equi- 
nox, and  when  the  autumnal  ? 


*  The  term  Equinoxes  strictly  denotes  the  times  when  the  sun  ar- 
rives at  the  equinoctial  points,  but  it  is  frequently  used  to  denote  those 
•"*nts  themselves. 


DOCTRINE  OF  THE  SPHERE.  15 

22.  The  Solstitial  Points  are  the  two  points  of  the 
ecliptic  most  distant  from  the  equator.     The  times  when 
the  sun  comes  to  them  are  called  solstices.     The  sum- 
mer solstice  occurs  about  the  22d  of  June,  and  the  win- 
ter solstice  about  the  22d  of  December. 

The  ecliptic  is  divided  into  twelve  equal  parts  of  30° 
each,  called  signs,  which,  beginning  at  the  vernal  equi- 
nox, succeed  each  other  in  the  following  order  : 

Northern.  Southern. 

1.  Aries  T  7.  Libra              £± 

2.  Taurus  S  8.  Scorpio          fl\. 

3.  Gemini  n  9.  Sagittarius      / 

4.  Cancer  <s  10.  Capricornus  K? 

5.  Leo  «fl  11.  Aquarius        #? 

6.  Virgo  TTJ?  12.  Pisces              ^ 

The  mocle  of  reckoning  on  the  ecliptic,  is  by  signs,  de- 
grees, minutes,  and  seconds.  The  sign  is  denoted  either 
by  its  name  or  its  number.  Thus  100°  maybe  express- 
ed either  as  the  10th  degree  of  Cancer,  or  as  3s  10°. 

23.  Of  the  various  meridians,  two  are  distinguished 
by  the  name  of  Colures.     The  Equinoctial   Colure,  is 
the  meridian   which    passes   through    the    equinoctial 
points.     From  this  meridian,  right  ascension  and  celes- 
tial longitude  are  reckoned,  as  longitude  on  the  earth  is 
reckoned  from  the  meridian  of  Greenwich.     The  Sol- 
stitial Colure,  is  the  meridian  which  passes  through  the 
solstitial  points. 

24.  The  position  of  a  celestial  body  is  referred  to  the 
equator  by  its  right  ascension  and  declination.     Right 

22,  Define  the  solstitial  points,  and  solstices.     When  does 
the  summer  solstice  occur  ?  when  does  the  winter  solstice  oc- 
cur 1     Into  how  many  signs  is  the  ecliptic  divided  ?     How 
many  degrees  are  there  in  each  ?     Name  the  signs.   What  is 
the  mode  of  reckoning  on  the  ecliptic  ?     In  what  two  wavs 
may  100°  be  expressed  ? 

23,  What  is  the  equinoctial  colure  ? — the  solstitial  colure  1 


16  THE  EARTH. 

Ascension,  is  the  angular  distance  from  the  vernal  equi- 
nox measured  on  the  equator.  If  a  star  is  situated  on 
the  equator,  then  its  right  ascension  is  the  number  of 
degrees  of  the  equator  between  the  star  and  the  vernal 
equinox.  But  if  the  star  is  north  or  south  of  the  equa- 
tor, then  its  right  ascension  is  the  arc  of  the  equator,  in- 
tercepted between  the  vernal  equinox  and  that  secon- 
dary to  the  equator  which  passes  through  the  star.  De- 
clination is  the  distance  of  a  body  from  the  equator, 
measured  on  a  secondary  to  the  latter.  Therefore,  right 
ascension  and  declination  correspond  to  terrestrial  longi- 
tude and  latitude,  right  ascension  being  reckoned  from 
the  equinoctial  colure,  in  the  same  manner  as  longitude 
is  reckoned  from  the  meridian  of  Greenwich.  On  the 
other  hand,  celestial  longitude  and  latitude  are  referred, 
not  to  the  equator,  but  to  the  ecliptic.  Celestial  Longi- 
tude, is  the  distance  of  a  body  from  the  vernal  equinox 
reckoned  on  the  ecliptic.  Celestial  Latitude,  is  distance 
from  the  ecliptic  measured  on  a  secondary  to  the  latter. 
Or,  more  briefly,  Longitude  is  distance  on  the  eclip- 
tic ;  Latitude,  distance  from  the  ecliptic.  The  North 
Polar  Distance  of  a  star,  is  the  complement  of  its  de- 
clination. 

25.  Parallels  of  Latitude  are  small  circles  parallel  to 
the  equator.  They  constantly  diminish  in  size  as  we  go 
from  the  equator  to  the  pole. 

The  Tropics  are  the  parallels  of  latitude  that  pass 
through  the  solstices.  The  northern  tropic  is  called  the 
tropic  of  Cancer  ;  the  southern,  the  tropic  of  Capricorn. 

The  Polar  Circles  are  the  parallels  of  latitude  that 
pass  through  the  poles  of  the  ecliptic,  at  the  distance  of 
23^  degrees  from  the  pole  of  the  earth. 


24.  Define  right  ascension  and  declination.     To  what  do 
they  correspond  on  the  terrestrial  sphere  ?     Define  celestia. 
longitude  and  latitude. 

25.  What  are  parallels  of  latitude — tropics — polar  circles  ? 
To  what  is  the  elevation  of  the  pole  always  equal  ?  also  that 
of  the  equator  ? 


DOCTRINE  OF  THE  SPHERE.  .  17 

The  elevation  of  the  pole  of  the  heavens  above  the 
horizon  of  any  place,  is  always  equal  to  the  latitude  of 
the  place.  Thus,  in  40°  of  north  latitude  we  see  the 
north  star  40°  above  the  northern  horizon,  whereas,  if 
we  should  travel  southward  its  elevation  would  grow 
less  and  less,  until  we  reached  the  equator,  where  it 
would  appear  in  the  horizon ;  or,  if  we  should  travel 
northward,  the  north  star  would  rise  constantly  higher 
and  higher,  until,  if  wre  could  reach  the  pole  of  the  earth, 
that  star  would  appear  directly  over  head.  The  eleva- 
tion of  the  equator  above  the  horizon  of  any  place,  is 
equal  to  the  complement  of  the  latitude.  Thus,  at  the 
latitude  of  40°  N.  the  equator  is  elevated  50°  above  the 
southern  horizon. 

26.  The  earth  is  divided  into  five  zones.     That  por- 
tion of  the  earth  which  lies  between  the  tropics,  is  called 
the  Torrid  Zone  ;  that  between  the  tropics  and   polar 
circles,  the   Temperate  Zones;   and    that    between  the 
polar  circles  and  the  poles,  the  Frigid  Zones. 

27.  The  Zodiac  is  the  part  of  the  celestial  sphere, 
which  lies  about  8  degrees  on  each  side  of  the  ecliptic. 
This  portion  of  the  heavens  is  thus  marked  off  by  itself, 
because  all  the  planets  move  within  it. 

28.  After  endeavoring  to  form,  from  the  definitions, 
as  clear  an  idea  as  he  can  of  the  various  circles  of  the 
sphere,  the  learner  may  next  resort  to  an  artificial  globe, 
and  see  how  they  are  severally  represented  there.     Or  if 
he  has  not  access  to  a  globe,  he  may  aid  his  conceptions 
by  the  following  easy  device.     To  represent  the  earth, 
select  a  large  apple,  (a   melon   when  in  season  will  be 
found  still  better.)     The  shape  of  the  apple,  flattened  as 


26.  Define  each  of  the  zones. 

27.  Define  the  zodiac. 

28.  Show  how  to  represent  the  artificial  sphere  by  any  round 
body,  as  an  apple,  and  point  out  the  various  circles  on  it. 

2* 


18  THE  EARTH. 


£ 


it  usually  is  at  the  two  ends,  will  not  inaptly  exhibit 
the  spheroidal  figure  of  the  earth,  while  the  larger  diam- 
ter  through  the  middle  will  indicate  the  excess  of  mat- 
r  about  the  equator ;  although  we  should  remark,  thai 
the  disproportion  between  the  polar  and  equatorial  diam 
eters  of  the  earth  is  in  fact  so  slight,  that  it  would  be 
scarcely  perceptible  in  a  model.  The  eye  and  the  stem 
of  the  apple  will  indicate  the  position  of  the  two  poles 
of  the  earth.  Applying  the  thumb  and  finger  of  the 
left  hand  to  the  poles,  and  holding  the  apple  so  that  the 
poles  may  be  in  a  north  and  south  line,  turn  the  globe 
from  west  to  east,  and  its  motion  will  correspond  to  the 
diurnal  movement  of  the  globe.  Pass  a  wire,  as  a  knit- 
ting needle,  through  the  poles,  and  it  will  represent  the 
axis  of  the  sphere.  A  circle  cut  around  the  apple  half 
way  between  the  poles,  will  be  the  equator  ;  and  several 
other  circles  cut  between  the  equator  and  the  poles,  par- 
allel to  the  equator,  will  represent  parallels  of  latitude, 
of  which,  two  drawn  23^  degrees  from  the  equator,  will 
be  the  tropics,  and  two  others  at  the  same  distance  from 
the  poles,  will  be  the  polar  circles.  A  great  circle  cut 
through  the  poles  in  a  north  and  south  direction,  will 
form  the  meridian,  and  several  other  great  circles  drawn 
through  the  poles,  and  of  course  perpendicularly  to  the 
equator,  will  be  secondaries  to  the  equator,  constituting 
meridians  or  hour  circles.  A  great  circle  cut  through  the 
center  of  the  earth  from  one  tropic  to  the  other,  will  rep- 
resent the  plane  of  the  ecliptic,  and  consequently,  a  line 
cut  around  the  apple  where  such  a  section  meets  the  sur- 
face, is  the  terrestrial  ecliptic.  The  points  where  this 
circle  meets  the  tropics,  are  the  solstices,  and  its  intersec- 
tions with  the  equator  are  the  equinoctial  points. 

29.  The  horizon  is  best  represented  by  a  circular 
piece  of  pasteboard,  cut  so  as  to  fit  closely  to  the  apple, 
being  movable  upon  it.  When  this  horizon  is  slipped 

29.  How  is  the  horizon  represented  in  our  model  ?  How  ia 
it  placed  to  represent  the  horizon  of  the  equator  ?  How  for  the 
horizon  of  the  poles  ?  How  for  our  own  horizon  ?  How  shall 
we  represent  the  prime  vertical  ? 


DOCTRINE  OF  THE  SPHERE. 


up  to  the  poles,  it  becomes  the  horizon  of  the  equator  ; 
when  it  is  so  placed  as  to  coincide  with  the  earth'? 
equator,  it  becomes  the  horizon  of  the  poles ;  and  in 
every  other  situation  it  represents  the  horizon  of  a  plac£ 
on  the  globe  90°  every  way  from  it.  Suppose  we  are 
in  latitude  40°,  then  let  us  place  our  movable  paper  par 
allel  to  our  own  horizon,  and  elevate  the  pole  40°  above 
it,  as  near  as  we  can  judge  by  the  eye.  If  we  cut  a  cir 
cle  around  the  apple,  passing  through  its  highest  parts 
and  through  the  east  and  west  points,  it  will  represent 
the  prime  vertical. 

30.  We  cannot  too  strongly  recommend  to  the  young 
learner  to  form  for  himself  such  a  sphere  as  is  here  de 
scribed,  and  to  point  out  on  it  the  various  arcs  of  azimuth 
and  altitude,  right  ascension  and  declination,  terrestrial 
and  celestial  latitude  and  longitude,  these  last  being  re 
ferred  to  the  equator  on  the  earth,  and  to  the  ecliptic  ir? 
the  heavens. 

31.  When  the  circles  of  the  sphere  are  well  learned 
we  may  advantageously  employ  projections  of  them  ir* 
various  illustrations.     By  the  projection  of  the  sphere  ifr 
meant  a  representation  of  all  its  parts  on  a  plane.     The 
plane  itself  is  called  the  plane  of  projection.     Let  us  take 
any  circular  ring,  as  a  wire  bent  into  a  circle,  and  hold 
it  in  different  positions  before  the  eye.     If  we  hold  it 
parallel  to  the  face,  or  directly  opposite  to  the  eye,  we 
see  it  as  an  entire  circle.     If  we  turn  it  a  little  sideways 
it  appears  oval,  or  as  an  ellipse ;  and  as  we  continue  tt 
turn  it  more  and  more  round,  the  ellipse  grows  narrower 
and  narrower,  until,  when  the  edge  is  presented  to  the 
eye,  we  see  nothing  but  a  line.     Now  imagine  the  rin§ 
to  be  near  a  perpendicular  wall,  and  the  eye  to  be  re 


80.  What  is  particularly  recommended  to  the  young  learner  « 
31    What  is  meant  by  the  projection  of  trj.Q  sphere  1     Wha 
is  the  projection  of  a  circle  when  seen  directly  before  the  face  \ 
what  when  seen  obliquely  1  what  when  seen  edgewise  1 


20 


THE  EARTH. 


moved  at  such  a  distance  from  it,  as  not  to  distinguish 
any  interval  between  the  ring  and  the  wall ;  then  the 
several  figures  under  which  the  ring  is  seen,  will  appear 
to  be  inscribed  on  the  wall,  and  we  shall  see  the  ring  as 
a  circle  when  perpendicular  to  a  straight  line  joining 
the  center  of  the  ring  and  the  eye,  as  an  ellipse  when 
oblique  to  this  line,  or  as  a  straight  line  when  its  edge  is 
towards  us. 

32.  It  is  in  this  manner  that  the  circles  of  the  sphere 
are  projected,  as  represented  in  the  following  diagram 


Here  various  circles  are  represented  as  projected  on  the 
meridian,  which  is  supposed  to  be  situated  directly  be- 
fore the  eye,  at  some  distance  from  it.  The  horizon  HO 
being  perpendicular  to  the  meridian  is  seen  edgewise,  and 
consequently  is  projected  into  a  straight  line.  The  same 
is  the  case  with  the  prime  vertical  ZN,  with  the  equator 
EQ,  and  the  several  small  circles  parallel  to  the  equator, 
which  represent  the  two  tropics  and  the  two  polar  cir- 


32.  In  figure  5,  what  represents  the  plane  of  projection  ? 
Why  are  certain  circles  represented  by  straight  lines  ?  why  are 
others  represented  by  ellipses  ?  How  is  the  eye  supposed  to 
be  situated  ? 


DIURNAL  REVOLUTION.  21 

cles.  In  fact,  all  circles  whatsoever,  which  are  perpen- 
dicular to  the  plane  of  projection,  will  be  represented 
by  straight  lines.  But  every  circle  which  is  perpendic- 
ular to  the  horizon,  except  the  prime  vertical,  being  seen 
obliquely  as  ZMN,  will  be  projected  into  an  ellipse. 
In  the  same  manner,  PRP,  an  hour  circle,  being  oblique 
to  the  eye,  is  represented  by  an  ellipse  on  the  plane  of 
projection. 


CHAPTER   II. 

DIURNAL  REVOLUTION ARTIFICIAL  GLOBES. 

33.  THE  apparent  diurnal  revolution  of  the  heavenly 
bodies  from  east  to  west,  is  owing  to  the  actual  revolu- 
tion of  the  earth  on  its  own  axis  from  west  to  east.     If 
we  conceive  of  a  radius  of  the  earth's  equator  extended 
until  it  meets  the  concave  sphere  of  the  heavens,  then 
as  the  earth  revolves,  the  extremity  of  this  line  would 
trace  out  a  curve  on  the  face  of  the  sky,  namely,  the  ce- 
lestial equator.     In  curves  parallel  to  this,  called  the  cir- 
cles of  diurnal  revolution,  the   heavenly  bodies  actually 
appear  to  move,  every  star  having  its  own  peculiar  cir- 
cle.    After  the  learner  has  first  rendered  familiar  the 
real  motions  of  the  earth  from  west  to  east,  he  may 
then,  without  danger  of  misconception,  adopt  the  com- 
mon language,  that   all   the   heavenly  bodies   revolve 
around  the  earth  once  a  day  from  east  to  west,  in  circles 
parallel  to  the  equator  and  to  each  other. 

34.  The  time  occupied  by  a  star  in  passing  from  any 
point  in  the  meridian  until  it  comes  round  to  the  same 


33.  To  what  is  the  apparent  diurnal  revolution  of  the  heav- 
enly bo.dies  from  east  to  west  owing  ?  If  a  radius  of  the  earth's 
equator  were  extended  to  meet  the  concave  sphere  of  the  heav- 
ens, what  would  it  trace  out  as  the  earth  revolves  ?  WhaJ 
are  circles  of  diurnal  revolution  ? 


22  THE  EARTH. 

point  again,  is  called  a  sidereal  day,  and  measures  the 
period  of  the  earth's  revolution  on  its  axis.  If  we  watch 
the  returns  of  the  same  star  from  day  to  day,  we  shall 
find  the  intervals  exactly  equal  to  one  another ;  that  is, 
the  sidereal  days  are  all  equal.  Whatever  star  we  se- 
lect for  the  observation,  the  same  result  will  be  obtained. 
The  stars,  therefore,  always  keep  the  same  relative  posi- 
tion, and  have  a  common  movement  round  the  earth — 
a  consequence  that  naturally  flows  from  the  hypothesis, 
that  their  apparent  motion  is  ajl  produced  by  a  single 
real  motion,  namely,  that  of  the  earth.  The  sun,  moon, 
and  planets,  as  well  the  fixed  stars,  revolve  in  like  man- 
ner, but  their  returns  to  the  meridian  are  not,  like  those 
of  the  fixed  stars,  at  exactly  equal  intervals. 

35.  The  appearances  of  the  diurnal  motions  of  the 
heavenly  bodies  are  different  in  different  parts  of  the 
earth,  since  every  place  has  its  own  horizon,  (Art.  8,) 
and  different  horizons  are  variously  inclined  to  each 
other.  Let  us  suppose  the  spectator  viewing  the  diurnal 
revolutions  from  several  different  positions  on  the  earth. 

On  the  equator,  his  horizon  would  pass  through  both 
poles ;  for  the  horizon  cuts  the  celestial  vault  at  90  de- 
grees in  every  direction  from  the  zenith  of  the  spectator  ; 
but  the  pole  is  likewise  90  degrees  from  his  zenith,  and 
consequently,  the  pole  must  be  in  the  horizon.  The  ce- 
lestial equator  would  coincide  with  the  Prime  Vertical, 


34.  Define  a  sidereal  day.     Are  the  sidereal  days  equal  or 
unequal  ?     Are  the   returns  of  the  sun,  moon,  and  planets  to 
the  meridian,  likewise  at  equal  intervals  ? 

35.  How  are  the  appearances  of  the  diurnal  motions  in  dif- 
ferent parts  of  the  earth  ?     When  the  spectator  is  on  the  equa- 
tor, where  would  his  horizon  pass  with  respect  to  the  poles  of 
the  earth  ?    With  what  great  circle  would  the  celestial  equator 
coincide  ?     How  would  all  the  circles  of  diurnal  revolution  be 
situated  with  respect  to  the  horizon  ?     Define  a  right  sphere. 
In  a  right  sphere,  how  would  a'star  situated  in  *he  celestial 
equator  perform  its  circuit  ?  how  would  stars  nearer  the  poles 
appear  to  move  1 


DIURNAL 

being  a  great  circle  passing  through  the  east  and  west 
points.  Since  all  the  diurnal  circles  are  parallel  to  the 
equator,  consequently,  they  would  all,  like  the  equator, 
be  perpendicular  to  the  horizon.  Such  a  view  of  the 
heavenly  bodies,  is  called  a  right  sphere  ;  or, 

A  RIGHT  SPHERE  is  one  in  which  all  the  daily  revolu- 
tions of  the  stars,  are  in  circles  perpendicular  to  the  horizon. 

A  right  sphere  is  seen  only  at  the  equator.  Any  star 
situated  in  the  celestial  equator,  would  appear  to  rise  di- 
rectly in  the  east,  when  on  the  meridian  to  be  in  the 
zenith  of  the  spectator,  and  to  set  directly  in  the  west ; 
in  proportion  as  stars  are  at  a  greater  distance  from  the 
equator  towards  the  pole,  they  describe  smaller  and 
smaller  circles,  until,  near  the  pole,  their  motion  is  hardly 
perceptible. 

36.  If  the  spectator  advances  one  degree  towards  the 
north  pole,  his  horizon  reaches  one  degree  beyond  the 
pole  of  the  earth,  and  cuts  the  starry  sphere  one  degree 
below  the  pole  of  the  heavens,  or  below  the  north  star, 
if  that  be  taken  as  the  place  of  the  pole.  As  he  moves 
onward  towards  the  pole,  his  horizon  continually  reaches 
farther  and  farther  beyond  it,  until  when  he  comes  to 
the  pole  of  the  earth,  and  under  the  pole  of  the  heavens, 
his  horizon  reaches  on  all  sides  to  the  equator  and  coin- 
cides with  it.  Moreover,  since  all  the  circles  of  daily 
motion  are  parallel  to  the  equator,  they  become,  to  the 
spectator  at  the  pole,  parallel  to  the  horizon.  This  is 
what  constitutes  a  parallel  sphere.  Or, 

A  PARALLEL  SPHERE  is  that  in  which  all  the  cwcles  of 
daily  motion  are  parallel  to  the  horizon. 

To  render  this  view  of  the  heavens  familiar,  the 
learner  should  follow  round  in  his  mind  a  number  of 


36.  What  changes  take  place  in  one's  horizon  as  he  moves 
from  the  equator  towards  the  pole  ?  How  would  it  be  situated 
when  he  reached  the  pole  ?  Define  a  parallel  sphere.  Explain 
the  appearances  of  the  stars  and  of  the  sun  in  a  parallel  sphere. 
Where  only  can  such  a  sphere  be  seen  ?  Has  the  pole  of  the 
earth  ever  been  reached  by  man  ? 


24  THE  EARTH. 

separate  stars,  one  near  the  horizon,  one  a  few  degrees 
above  it,  and  a  third  near  the  zenith.  To  one  who 
stood  upon  the  north  pole,  the  stars  of  the  northern  hemi- 
sphere would  all  be  perpetually  in  view  when  not  ob- 
scured by  clouds  or  lost  in  the  sun's  light,  and  none  of 
those  of  the  southern  hemisphere  would  ever  be  seen. 
The  sun  would  be  constantly  above  the  horizon  for  six 
months  in  the  year,  and  the  •  remaining  six  constantly 
out  of  sight.  That  is,  at  the  pole  the  days  and  nights 
are  each  six  months  long.  The  phenomena  at  the  south 
pole  are  similar  to  those  at  the  north. 

A  perfect  parallel  sphere  can  never  be  seen  except  at 
one  of  the  poles — a  point  which  has  never  been  actually 
reached  by  man  ;  yet  the  British  discovery  ships  pene- 
trated within  a  few  degrees  of  the  north  pole,  and  of 
course  enjoyed  the  view  of  a  sphere  nearly  parallel. 

37.  As  the  circles  of  daily  motion  are  parallel  to  the 
lorizon  of  the  pole,  and  perpendicular  to  that  of  the 
equator,  so  at  all  places  between  the  two,  the  diurnal 
motions  are  oblique  to  the  horizon.  This  aspect  of  the 
neavens  constitutes  an  oblique  sphere,  which  is  thus  de- 
nned : 

An  OBLIQUE  SPHERE  is  that  in  which  the  circles  of 
iaily  motion  are  oblique  to  the  horizon. 

Suppose,  for  example,  the  spectator  is  at  the  latitude  of 
<ifty  degrees.  His  horizon  reaches  50°  beyond  the  pole 
:>f  the  earth,  and  gives  the  same  apparent  elevation  to 
die  pole  of  the  heavens.  It  cuts  the  equator,  and  all 
che  circles  of  daily  motion,  at  an  angle  of  40°,  being  al- 
ways equal  to  the  co-altitude  of  the  pole.  Thus,  let  HO 
'vFig.  6,)  represent  the  horizon,  EQ  the  equator,  and 
PP'  the  axis  of  the  earth.  Also,  //,  mm,  &c.,  parallels 
of  latitude.  Then  the  horizon  of  a  spectator  at  Z,  in 
'atitude  50°  reaches  to  50°  beyond  the  pole ;  and  the 
ingle  ECH,  is  40°.  As  we  advance  still  farther  north 


37.  Define  an  oblique  sphere.     Where  is  it  seen  ?     At  the 
latitude  of  50°  how  is  the  horizon  situated  ?    Illustrate  by  fig.  6 


DIURNAL  REVOLUTION. 

Fig.  6. 


25 


the  e.evation  of  the  diurnal  circles  grows  less  and  less, 
and  consequently  the  motions  of  the  heavenly  bodies 
more  and  more  oblique,  until  finally,  at  the  pole,  where 
the  latitude  is  90°,  the  angle  of  elevation  of  the  equator 
vanishes,  and  the  horizon  and  equator  coincide  with 
each  other,  as  Before  stated. 

38.  The  CIRCLE  OP  PERPETUAL  APPARITION,  is  the 
boundary  of  that  space  around  the  elevated  pole,  where 
the  stars  never  set.  Its  distance  from  the  pole  is  equal 
to  the  latitude  of  the  place.  For,  since  the  altitude  of 
the  pole  is  equal  to  the  latitude,  a  star  whose  polar  dis- 
tance is  just  equal  to  the  latitude,  will  when  at  its  low- 
est point  only  just  reach  the  horizon ;  and  all  the  stars 
nearer  the  pole  than  this  will  evidently  not  descend  so 
far  as  the  horizon. 

Thus,  mm  (Fig.  6,)  is  the  circle  of  perpetual  appari- 
tion, between  which  and  the  north  pole,  the  stars  never 
set,  and  its  distance  from  the  pole  OP  is  evidently  equal 
to  the  elevation  of  the  pole,  and  of  course  to  the  lati- 
tude. 


38.  What  is  the  circle  of  perpetual  apparition  ? 
by  fig.  6. 

3 


I.lustrate 


26  THE  EARTH. 

39.  In  the  opposite  hemisphere,  a  similar  part  of  the 
sphere  adjacent  to  the  depressed  pole  never  rises.  Hence 

The  CIRCLE  OF    PERPETUAL    OCCULTATION,  IS    the    boUH* 

dary  of  that  space  around  the  depressed  pole,  within 
which  the  stars  never  rise.  Thus,  m'm  (Fig.  6,)  is  the 
circle  of  perpetual  occultation,  between  which  and  the 
south  pole,  the  stars  never  rise. 

40.  In  an  oblique  sphere,  the  horizon  cuts  the  circles 
of  daily  motion  unequally.     Towards  the  elevated  pole, 
more  than  half  the  circle  is  above  the  horizon,  and  a 
greater  and  greater  portion  as  the  distance  from  the 
equator  is  increased,  until  finally,  within  the  circle  of 
perpetual  apparition,  the  whole  circle  is  above  the  hori- 
zon.    Just  the  opposite  takes  place  in  the  hemisphere 
next  the  depressed  pole.     Accordingly,  when  the  sun  is 
in  the  equator,  as  the  equator  and  horizon,  like  all  other 
great  circles  of  the  sphere,  bisect  each  other,  the  days 
and  nights  are  equal  all  over  the  globe.     But  when  the 
sun  is  north  of  the  equator,  the  days  become  longer  than 
the  nights,  but  shorter  when  the  sun  4s  south  of  the 
equator.     Moreover,  the  higher  the  latitude,  the  greater 
is  the  inequality  in  the  lengths  of  the  days  and  nights. 
All  these  ooints  will  be  readily  understood  by  inspecting 
figure  6 

41.  Most  of  the  appearances  of  the  diurnal  i  evolution 
can  be  explained,  either  on  the  supposition  that  the  ce- 
lestial sphere  actually  all  turns  around  the  earth  once  in 
24  hours,  or  that  this  motion  of  the  heavens  is  merely 
apparent,  arising  from  the  revolution  of  the  earth  on  its 


39.  What  is  the  circle  of  perpetual  occultation  ?     Illustrate 
by  fig.  6. 

40.  How  does  the  horizon  of  an  oblique  sphere  cut  the  cir- 
cles of  daily  motion  ?    Towards  the  elevated  pole  what  r»ortion 
of  the  circles  is  above  the  horizon  ?     Towards  the  depressed 
pole,  how  is  the  fact?     When  are  the  days  and  nights  equal 
all  over  the  world  ?     When  are  the  days  longer,  and  when 
shorter  than  the  nights  ? 


DIURNAL  REVOLUTION.  27 

axis  in  the  opposite  direction — a  motion  of  which  we 
are  insensible,  as  we  sometimes  lose  the  consciousness 
of  our  own  motion  in  a  ship  or  a  steamboat,  and  observe 
•all  external  objects  to  be  receding  from  us  with  a  com- 
mon motion.  Proofs  entirely  conclusive  and  satisfac- 
tory, establish  the  fact,  that  it  is  the  earth  and  not  the 
celestial  sphere  that  turns  ;  but  these  proofs  are  drawn 
from  various  sources,  and  the  student  is  not  prepared  to 
appreciate*  their  value,  or  even  to  understand  some  of 
them,  until  he  has  made  considerable  proficiency  in  the 
study  of  astronomy,  and  become  familiar  with  a  great 
variety  of  astronomical  phenomena.  To  such  a  period 
of  our  course  of  instruction,  we  therefore  postpone  the 
discussion  of  the  hypothesis  of  the  earth's  rotation  on 
its  axis. 

42.  While  we  retain  the  same  place  on  the  earth,  the 
diurnal  revolution  occasions  no  change  in  our  horizon, 
but  our  horizon  goes  round  as  well  as  ourselves.  Let 
us  first  take  our  station  on  the  equator  at  sunrise ;  our 
horizon  now  passes  through  both  the  poles,  and  through 
the  sun,  which  we  are  to  conceive  of  as  at  a  great  dis- 
tance from  the  earth,  and  therefore  as  cut,  not  by  the 
terrestrial  but  by  the  celestial  horizon.  As  the  earth 
turns,  the  horizon  dips  more  and  more  below  the  sun,  at 
the  rate  of  15  degrees  for  every  hour,  and,  as  in  the  case 
of  the  polar  star,  the  sun  appears  to  rise  at  the  same  rate. 
In  six  hours,  therefore,  it  is  depressed  90  degrees  below 
the  sun,  which  brings  us  directly  under  the  sun,  which, 
for  our  present  purpose,  we  may  consider  as  having  all 
the  while  maintained  the  same  fixed  position  in  space 


4 1 .  On  what  suppositions  can  the  appearances  of  the  diurna. 
revolution  be  explained  ?     Is  it  the  earth  or  the  heavens  tha 
really  move  ?    Why  is  the  discussion  of  this  subject  postponed  ? 

42.  Explain  the  true  cause  of  the  sun's  appearing  to  rise  and 
set,  as  observed  at  the  equator.     What  is  the  position  of  the  ho- 
rizon at  sunrise  ?     What    at  six  hours  afterwards  ?     What  a 
the  end  of  twelve  hours  ?   What  at  the  end  of  eighteen  hours' 


28  THE  EARTH. 

The  earth  continues  to  turn,  and  in  six  hours  more,  it 
completely  reverses  the  position  of  our  horizon,  so  that 
the  western  part  of  the  horizon  which  at  sunrise  was 
diametrically  opposite  to  the  sun  now  cuts  the  sun,  and 
soon  afterwards  it  rises  above  the  level  of  t-he  sun,  anci 
the  sun  sets.  During  the  next  twelve  hours,  the  sun 
continues  on  the  invisible  side  of  the  sphere,  until  the 
horizon  returns  to  the  position  from  which  it  started,  and 
a  new  day  begins. 

43.  Let  us  next  contemplate  the  similar  phenomena 
at  the  poles.  Here  the  horizon,  coinciding  as  it  does 
with  the  equator,  would  cut  the  sun  through  its  center, 
and  the  sun  would  appear  to  revolve  along  the  surface 
of  the  sea,  one-half  above  and  the  other  half  below  the 
horizon.  This  supposes  the  sun  in  its  annual  revolution 
to  be  at  one  of  the  equinoxes.  When  the  sun  is  north 
of  the  equator,  it  revolves  continually  round  in  a  circle, 
which,  during  a  single  revolution,  appears  parallel  to  the 
equator,  and  it  is  constantly  day ;  and  when  the  sun 
is  south  of  the  equator,  it  is,  for  the  same  reason,  contin- 
ual night. 

We  have  endeavored  to  conceive  of  the  manner  in 
which  the  apparent  diurnal  movements  of  the  sun  are 
really  produced  at  two  stations,  namely,  in  the  right 
sphere,  and  in  the  parallel  sphere.  These  two  cases 
being  clearly  understood,  there  will  be  little  difficulty  in 
applying  a  similar  explanation  to  an  oblique  sphere. 


ARTIFICIAL  GLOBES. 

44.  Artificial  globes  are  of  two  kinds,  terrestrial  and 
celestial.  The  first  exhibits  a  miniature  representation 
of  the  earth  ;  the  second,  of  the  visible  heavens  ;  and 
both  show  the  various  circles  by  which  the  two  spheres 


43.  Explain  the  similar  phenomena  at  the  poles,  first,  when 
the  sun  is  at  the  equinoxes,  and  secondly,  when  it  is  north  and 
when  it  is  south  of  the  equator. 


ARTIFICIAL  GLOBES.  29 

are  respectively  traversed  Since  all  globes  are  similar 
solid  figures,  a  small  globe,  imagined  to  be  situated  at 
the  center  of  the  earth  or  of  the  celestial  vault,  may  rep- 
resent all  the  visible  objects  and  artificial  divisions  of 
either  sphere,  and  with  great  accuracy  and  just  propor- 
tions, though  on  a  scale  greatly  reduced.  The  study  of 
artificial  globes,  therefore,  cannot  be  too  strongly  recom- 
mended to  the  student  of  astronomy.* 

45.  An  artificial  globe  is  encompassed  from  north  to 
south  by  a  strong  brass  ring  to  represent  the  meridian  of 
the  place.  This  ring  is  made  fast  to  the  two  poles  and 
thus  supports  the  globe,  while  it  is  itself  supported  in  a 
vertical  position  by  means  of  a  frame,  the  ring  being 
usually  let  into  a  socket  in  which  it  may  be  easily  slid, 
so  as  to  give  any  required  elevation  to  the  pole.  The 
brass  meridian  is  graduated  each  way  from  the  equator 
to  the  pole  90°,  to  measure  degrees  of  latitude  or  decli- 
nation, according  as  the  distance  from  the  equator  refers 
to  a  point  on  the  earth  or  in  the  heavens.  The  horizon 
is  represented  by  a  broad  zone,  made  broad  for  the  con- 
venience of  carrying  on  it  a  circle  of  azimuth,  another  of 
amplitude,  and  a  wide  space  on  which  are  delineated 
the  signs  of  the  ecliptic,  and  the  sun's  place  for  every 
day  in  the  year  ;  not  because  these  points  have  any  spe- 
cial connexion  with  the  horizon,  but  because  this  broad 
surface  furnishes  a  convenient  place  for  recording  them. 


44.  What  does  the  terrestrial  globe   exhibit  ?     What  does 
the  celestial  globe  ?     What  do  both  show  ? 

45.  How  is  the  meridian  of  the  place  represented  ?  To  what 
points  is  the  brass  meridian  fastened  ?   What  supports  the  ring  ? 
How  is  it  graduated  ?  How  is  the  horizon  represented  ?  Why 
is  it  made  broad  ?     What  circles  are  inscribed  on  it  ? 


*  Tt  were  Desirable,  indeed,  that  every  student  of  the  science  should 
have  a  celestial  globe,  at  least,  constantly  before  him.  One  of  a 
small  size,  as  eight  or  nine  inches,  will  answer  the  purpose,  although 
globes  of  these  dimensions  cannot  usually  be  relied  on  for  nice  meas- 
urements 

3* 


SO  THE  EARTH. 

46.  Hour  Circles  are  represented  on  the  terrestrial 
globe  by  great  circles  drawn  through  the  pole  of  the 
equator  ;  but,  on  the  celestial  globe,  corresponding  cir- 
cles pass  through  the  poles  of  the  ecliptic,  constituting 
circles  of  latitude,  while  the  brass  meridian,  being  a  se- 
condary to  the  equinoctial,  becomes  an  hour  circle  of 
any  star  which,  by  turning  the  globe,  is  brought  under  it. 

47.  The  Hour  Index  is  a  small  circle  described  around 
the  pole  of  the  equator,  on  which  are  marked  the  hours 
of  the  day.     As  this  circle  turns  along  with  the  globe,  it 
makes  a  complete  revolution  in  the  same  time  with  the 
equator  ;  or,  for  any  less  period,  the  same  number  of  de- 
grees of  this  circle  and  of  the  equator  pass  under  the 
meridian.     Hence  the  hour  index  measures  arcs  of  right 
ascension,  15°  passing  under  the  meridian  every  hour. 

48.  The   Quadrant  of  Altitude  is  a  flexible  strip  of 
brass,  graduated  into  ninety  equal  parts,  corresponding 
in  length  to  degrees  on  the  globe,  so  that  when  applied  to 
the  globe  *nd  bent  so  as  closely  to  fit  its  surface,  it  meas- 
ures the  angular   distance   between  any   two   points. 
When  the  zero,  or  the  point  where  the  graduation  be- 
gins, is  laid  on  the  pole  of  any  great  circle,  the  90th  de- 
gree will  reach  to  the  circumference  of  that  circle,  and 
being  therefore  a  great  circle  passing  through  the  pole 
of  another  great  circle,  it  becomes  a  secondary  to  the 
latter.     Thus  the  quadrant  of  altitude  may  be  used  as  a 
secondary  to  any  great  circle  on  the  sphere  ;  but  it  is 
used  chiefly  as  a  secondary  to  the  horizon,  the  point 


46.  How   are   hour   circles  represented  on  the   terrestrial 
globe  ?  How  are  circles  of  latitude  represented  on  the  celes- 
tial globe  ? 

47.  Describe  the  hour  index.     What  does  it  measure  ? 

48.  What  is  the  quadrant  of  altitude?     How  is  it  gradua 
ted  ?  When  the  zero  point  is  laid  on  the  pole  of  any  great  cir- 
cle, to  what  will  the  90th  degree  reach  ?  How  may  it  be  used 
as  a  secondary  to  any  great  circle  ?     When  screwed  on  the 
zenith  what  does  it  become  ?  What  arcs  does  it  then  measure  ? 


TERRESTRIAL  GLOBE.  31 

marked  90°  being  screwed  fast  to  the  pole  of  the  hori- 
zon, that  is,  the  zenith,  and  the  other  end,  marked  0. 
being  slid  along  between  the  surface  of  the  sphere  and 
the  wooden  horizon.  It  thus  becomes  a  vertical  circle, 
on  which  to  measure  the  altitude  of  any  star  through 
which  it  passes,  or  from  which  to  measure  the  azimuth 
of  the  star,  which  is  the  arc  of  the  horizon  intercepted 
between  the  meridian  and  the  quadrant  of  altitude  pass- 
ing through  the  star. 

49.  To  rectify  the.  globe  for  any  place,  the  north  pole 
must  be  elevated  to  the  latitude  of  the  place  ;  then  the 
equator  and  all  the  diurnal  circles  will  have  their  due  in- 
clination in  respect  to  the  horizon  ;  and,  on  turning  the 
globe,  every  point  on  either  globe  will  revolve  as  the 
same  point  does  in  nature ;  and  the  relative  situations  of 
all  places  will  be  the  same  as  on^the  native  spheres. 

PROBLEMS  ON  THE  TERRESTRIAL  GLOBE. 

50.  To  find  the  Latitude  and  Longitude  of  a  place  : 
Turn  the  globe  so  as  to  bring  the  place  to  the  brass  me- 
ridian ;  then  the  degree  and  minute  on  the  meridian  di- 
rectly over  the  place  will  indicate  its  latitude,  and  the 
point  of  the  equator  under  the  meridian,  will  show  its 
longitude. 

Ex.  What  is  the  Latitude  and  Longitude  of  the  city 
of  New  York? 

51.  To  find  a  place  having  its  Latitude  and  Longitude 
given :  Bring  to  the  brass  meridian  the  point  of  the  equa- 
tor corresponding  to  the  longitude,  and  then  at  the  de- 
gree of  the  meridian  denoting  the  latitude,  the  place  will 
be  found. 

Ex.  What  place  on  the  globe  is  in  Latitude  39°  N.  and 
Longitude  77°  W.  ? 


49.  How  do  we  rectify  the  globe  for  any  place  ? 

50.  Find  the  latitude  and  longitude  of  Washington  City. 

51.  What  place  lies  in  latitude  39°  N.  and  longitude  77°  W.? 


32  THE  EARTH. 

52.  To  find  the  bearing  and  distance  of  two  places  : 
Rectify  the  globe  for  one  of  the  places  ;  screw  the  quad- 
rant of  altitude  to  the  zenith,*  and  let  it  pass  through 
the  other  place.     Then  the  azimuth  will  give  the  bear- 
ing of  the  second  place  from  the  first,  and  the  number 
of  degrees  on  the  quadrant  of  altitude,  multiplied  by  69, 
(the  number  of  miles  in  a  degree,)  will  give  the  distance 
between  the  two  places. 

Ex.  What  is  the  bearing  of  New  Orleans  from  New 
York,  and  what  is  the  distance  between  these  places  ? 

53.  To  determine  the  difference  of  time   in  different 
places :  Bring  the  place  that  lies  eastward  of  the  other 
to  the  meridian,  and  set  the  hour  index  at  XII.     Turn 
the  globe  eastward  until  the  other  place  comes  to  the 
meridian,  then  the  index  will  point  to  the  hour  required. 

Ex.  When  it  is  noon  at  New  York,  what  time  is  it  at 
London  ? 

54.  The  hour  being  given  at  any  place,  to  tell  what 
hour  it  is  in  any  other  part  of  the  world :  Bring  the 
given  place  to  the  meridian,  and  set  the  hour  index  to 
the  given  time  ;  then  turn  the  globe,  until  the   other 
place  comes  under  the  meridian,  and  the   index  will 
point  to  the  required  hour. 

Ex.  What  time  is  it  at  Canton,  in  China,  when  it  is 
9  o'clock  A.  M.  at  New  York  ? 

55.  To  find  what  people  on  the  earth  live  under  us, 
having  their  noon  at  the  time  of  our  midnight :  Bring 
the  place  where  we  dwell  to  the  meridian,  and  set  the 


52.  What  is  the  bearing  and  distance  of  New  Orleans  from 
New  York  ? 

53.  When  it  is  noon  at  New  York,  what  time  is  it  at  Pekin  ? 
54   What  time  is  it  at  London  when  it  is  noon  at  Boston  ? 


*  The  zenith  will  of  course  be  the  point  of  the  meridian  over  the 
place. 


TERRESTRIAL  GLOBE.  33 

hour  index  to  XII ;  then  turn  the  globe  until  the  other 
XII  comes  under  the  meridian;  the  point  under  the 
same  part  of  the  meridian  where  we  were  before,  will 
be  the  place  sought. 

Ex.  Find  what  place  is  directly  under  New  York. 

56.  To  find  what  people  of  the  southern  hemisphere 
are  directly  opposite  to  us :  Bring  our  place  to  the  me- 
ridian ;  the  place  in  the  same  latitude  south,  then  un- 
der the  meridian,  will  be  the  place  in  question. 

Ex.  What  place  in  the  southern  hemisphere  corres- 
ponds to  New  Haven  ? 

57.  To  find  the  antipodes  of  a  place,  or  the  people 
whose  feet  are  exactly  opposite  to  ours  :  Bring  our  place 
to  the^meridian ;  set  the  hour  index  to  XII,  and  turn  the 
globe  until  J;he  other  XII  comes  under  the  meridian; 
then  the  point  of  the  southern  hemisphere  under  the  me- 
ridian and  having  the  same  latitude  with  ours,  will  be 
the  place  of  our  antipodes. 

Ex.  Who  are  antipodes  to  the  people  of  Philadelphia  ? 

58.  To  rectify  the  globe  for  the  sun9s  place :  On  the 
wooden  horizon,  find  the  day  of  the  month,  and  against 
it  is  given  the  sun's  place  in  the  ecliptic,  expressed  by 
signs  and  degrees.*     Look  for  the  same  sign  and  degree 
on  the  ecliptic,  bring  that  point  to  the  meridian  and  set 
the  hour  index  to  XII.     To  all  places  under  the  merid- 
ian it  will  then  be  noon, 

Ex.  Rectify  the  globe  for  the  sun's  place  on  the  1st 
of  September. 


55.  Find  what  place  is  directly  under  Philadelphia. 

56.  What  place  in  south  latitude  corresponds  to  Boston  ? 

57.  Who  are  the  antipodes  of  the  people  of  London  ? 

58.  Rectify  the  globe  for  the  sun's  place  for  the  first  of  June 


*  The  larger  globes  have  the  day  of  the  month  marked  against  the 
corresponding  sign  on  the  ecliptic  itself. 


34  THE  EARTH. 

59.  Tne  latitude  of  the  place  being  given,  to  find  the 
time  of  the  sun's  rising  and  setting  on  a.ny  given  day 
at  that  place :  Having  rectified  the  globe  for  the  lati- 
tude, bring  the  sun's  place  in  the  ecliptic  to  the  gradua- 
ted edge  of  the  meridian,  and  set  the  hour  index  to  XII ; 
then  turn  the  globe  so  as  to  bring  the  sun  to  the  eastern 
and  then  to  the  western  horizon,  and  the  hour  index 
will  show  the  times  of  rising  and  setting  respectively. 

Ex.  At  what  time  will  the  sun  rise  and  set  at  New 
Haven,  Lat.  41°  18',  on  the  10th  of  July  ? 

PROBLEMS  ON  THE  CELESTIAL  GLOBE. 

60.  To  find  the  Declination  and  Right  Ascension  oj 
a  heavenly  body :  Bring  the  place  of  the  body  (whether 
sun  or  star)   to  the  meridian.     Then  the   degree  and 
minute  standing  over  it  will  show  its  declination,  and 
the  point  of  the  equinoctial  under  the  meridian  will  give 
its  right  ascension.     It  will  be  remarked,  that  the  decli- 
nation and  right  ascension  are  found  in  the  same  man- 
ner as  latitude  and  longitude  on  the  terrestrial  globe. 
Right  ascension,  is  expressed  either  in  degrees  or  in 
hours  ;  both  being  reckoned  from  the  vernal  equinox. 

Ex.  What  is  the  declination  and  right  ascension  of  the 
bright  star  Lyra? — also  of  the  sun  on  the  5th  of  June? 

61.  To  represent  the  appearance  of  the  heavens  at  any 
time  :  Rectify  the  globe  for  the  latitude,  bring  the  sun's 
place  in  the  ecliptic  to  the  meridian,  and  set  the  hour 
index  to  XII ;  then  turn  the  globe  westward  until  the 
index  points  to  the  given  hour,  and  the  constellations 
would  then  have  the  same  appearance  to  an  eye  situated 


59.  Find  the  time  of  the  sun's  rising  and  setting  at  Boston 
(Lat,  42°,  Lon.  71°)  on  the  first  day  of  December. 

60.  On  the  celestial  globe,  What  is  the  right  ascension  and 
declination  of  any  star  taken  at  pleasure  ? 

61.  Represent  the  appearanceof  the  heavens  at  Tuscaloosa 
(Lat.  33°,  Lon.  87°)  at  8  o'clock  in  the  evening  of  Nov.  13th, 


CELESTIAL  GLOBE.  35 

at  the  center  of  the  globe,  as  they  have  at  that  moment 
in  the  sky. 

Ex.  Required  the  aspect  of  the  stars  at  New  Haven, 
Lat.  41°  18',  at  10  o'clock,  on  the  evening  of  Decem- 
ber 5th. 

62.  To  find  the  altitude  and  azimuth   of  any  star . 
Rectify  the  globe  for  the  latitude,  and  let  the  quadrant 
of  altitude  be  screwed  to  the  zenith,  and  be  made  to  pass 
through  the  star.     The  arc  on  the  quadrant,  from  the 
horizon  to  the  star,  will  denote  its  altitude,  and  the  arc 
of  the  horizon  from  the  meridian  to  the  quadrant,  will  be 
its  azimuth. 

Ex.  What  is  the  altitude  and  azimuth  of  Sirius  (the 
brightest  of  the  fixed  stars)  on  the  25th  of  December  at 
10  o'clock  in  the  evening,  in  Lat.  41°  ? 

63.  To  find  the  angular  distance  of  two  stars  from 
each  other  :  Apply  the  zero  mark  of  the  quadrant  of  alti- 
tude to  one  of  the  stars,  and  the  point  of  the  quadrant 
which  falls  on  the  other  star,  will  show  the  angular  dis- 
tance between  the  two. 

Ex.  What  is  the  distance  between  the  two  largest 
stars  of  the  Great  Bear.* 

64.  To  find  the  sun's  meridian  altitude,  the  latitude 
and  day  of  the  month  being  given :   Having  rectified 
the  globe  for  the  latitude,  bring  the  sun's  place  in  the 
ecliptic  to  the  meridian,  and  count  the   number  of  de- 


62.  Find  the  altitude  and  azimuth  of  Lyra  at  10  o'clock  in 
the  evening  of  June  1 8th,  in  Lat.  42°. 

63.  Find  the  angular  distance  between  any  two  stars  taken 
at  pleasure. 


*  These  two  stars  are  sometimes  called  "the  Pointers,"  from  the  line 
which  passes  through  them  being  always  nearly  in  the  direction  of  the 
north  star.  The  angular  distance  between  them  is  about  5°,  and  may 
be  learned  as  a  standard  of  reference  in  estimating  by  the  eye,  the  dis- 
tance between  any  two  points  on  the  celestial  vault. 


36 


THE  EARTH. 


grees  and  minutes  between  that  point  of  the  meridian 
and  the  zenith.  The  complement  of  this  arc  will  be 
the  sun's  meridian  altitude. 

Ex.  What  is  the  sun's  meridian  altitude  at  noon  on 
the  1st  of  August,  in  Lat.  41°  18/  ? 


CHAPTER    III. 

OP  PARALLAX,  REFRACTION,  AND  TWILIGHT. 

65.  PARALLAX  is  the  apparent  change  of  place  which 
bodies  undergo  by  being   viewed   from   different  points. 


Fig.  7. 


Thus  in  figure  7,  let  A  represent  the  earth,  CH  the  ho- 
rizon.    HZ  a  quadrant  of  a  great  circle  of  the  heavens, 


64.  What  is  the  sun's  meridian  altitude  at  noon  on  the  18th 
of  June,  in  latitude  35°  ? 

65.  Define  parallax.     Illustrate  by  the  figure.     What  angle 
measures  the  parallax?     Why  do  astronomers  consider  the 
heavenly  bodies  as  viewed  from  the  center  of  the  earth  ? 


PARALLAX.  37 

extending  from  the  horizon  to  the  zenith ;  and  let  E,  F, 
G,  O,  be  successive  positions  of  the  moon  at  different 
elevations,  from  the  horizon  to  the  meridian.  Now  a 
spectator  on  the  surface  of  the  earth  at  A,  would  refer 
the  place  of  E  to  h,  whereas,  if  seen  from  the  center  of 
the  earth,  it  would  appear  at  H.  The  arc  H/i  is  called 
the  parallactic  arc,  and  the  angle  HE/i,  or  its  equal  AEC, 
is  the  angle  of  parallax.  The  same  is  true  of  the  angles 
at  F,  G,  and  O,  respectively. 

Since  then  a  heavenly  body  is  liable  to  be  referred  to 
different  points  on  the  celestial  vault,  when  seen  from 
differe-nt  parts  of  the  earth,  and  thus  some  confusion 
occasioned  in  the  determination  of  points  on  the  celes- 
tial sphere,  astronomers  have  agreed  to  consider  the  true 
place  of  a  celestial  object  to  be  that,  where  it  would 
appear  if  seen  from  the  center  of  the  earth.  The  doc- 
trine of  parallax  teaches  how  to  reduce  observations 
made  at  any  place  on  the  surface  of  the  earth,  to  such  as 
hey  would  be  if  made  from  the  center. 

66.  The  angle  AEC  is  called  the  horizonta  parallax, 
which  may  be  thus  defined.  Horizontal  Parallax,  is 
the  change  of  position  which  a  celestial  body,  appearing 
in  the  horizon  as  seen  from  the  surface  of  the  earth, 
would  assume  if  viewed  from  the  earth's  center.  It  is 
the  angle  subtended  by  the  semi-diameter  of  the  earth, 
as  viewed  from  the  body  itself. 

It  is  evident  from  the  figure/that  the  effect  of  parallax 
upon  the  place  of  a  celestial  body  is  to  depress  it.  Thus, 
in  consequence  of  parallax,  E  is  depressed  by  the  arc 
Hh  ;  F  by  the  arc  Pp  ;  G  by  the  arc  Rr ;  while  O  sus- 
tains no  change.  Hence,  in  all  observations  on  the  al- 
titude of  the  sun,  moon,  or  planets,  the  amount  of  par- 
allax is  to  be  added :  the  stars,  as  we  shall  see  here- 
after, have  no  sensible  parallax. 


66.  Define  horizontal  parallax — By  what  is  it  subtended? 
(See  Art.  10.  Note.)  What  is  the  effect  of  parallax  upon  the 
place  of  a  heavenly  body? 

4 


38 


THE  EARTH. 


67.  The  determination  of  the  horizontal  parallax  of  a 
celestial  body  is  an  element  of  great  importance,  since  it 
furnishes  the  means  of  estimating  the  distance  of  the 
body  from  the  center  of  the  earth.     Thus,  if  the  angle 
AEC  (Fig  7,)  be  found,  the  radius  of  the  earth  AC  be- 
ing known,  we  have  in  the  right  angled  triangle  AEC, 
the  side  AC  and  all  the  angles,  to  find  the  side  CE, 
which  is  the  distance  of  the  moon  from  the  center  ot 
the  earth.* 

REFRACTION. 

68.  While  parallax  depresses  the  celestial  bodies  sub* 
ject  to  it,  refraction  elevates  them;  and  it  affects  alike 
the  most  distant  as  well  as  nearer  bodies,  being  occa- 
sioned by  the  change  of  direction  which  light  undergoes 

Fig.  8. 


67.  Why  is  the  determination  of  the  parallax  of  a  heavenly 
body  an  element  of  great  importance  ?     Illustrate  by  figure  7. 


*  Should  the  reader  be  unacquainted  with  the  principles  of  trigonom- 
etry, yet  he  ought  to  know  the  fact  that  these  principles  enable  us, 
when  we  have  ascertained  certain  parts  in  a  triangle,  to  find  the  un- 
known parts.  Thus,  in  the  above  case,  when  we  have  found  the  an- 
gle of  parallax,  AEB,  (which  is  determined  by  certain  astronomical  ob- 
servations,) knowing  also  the  semi-diameter  of  the  earth  AC,  we  can 
find  by  trigonometry,  the  length  of  the  side  CE,  which  is  the  distance 
of  the  body  from  the  center  of  the  earth. 


REFRACTION.  39 

in  passing  through  the  atmosphere.  Let  us  conceive  of 
the  atmosphere  as  made  up  of  a  great  number  of  concen- 
tric strata,  as  AA,  BB,  CC,  and  DD,  (Fig.  8,)  increasing 
rapidly  in  density  (as  is  known  to  be  the  fact)  in  ap- 
proaching near  to  the  surface  of  the  earth.  Let  S  be  a 
star,  from  which  a  ray  of  light  Sa  enters  the  atmosphere 
at  a,  where,  being  much  turned  towards  the  radius  of 
the  convex  surface,*  it  would  change  its  direction  into 
the  line  «&,  and  again  into  6c,  and  cO,  reaching  the 
eye  at  O.  Now,  since  an  object  always  appears  in  the 
direction  in  which  the  light  finally  strikes  the  eye,  the 
star  would  be  seen  in  the  direction  of  the  ray  Oc,  and 
therefore,  the  star  would  apparently  change  its  place, 
in  consequence  of  refraction,  from  S  to  S',  being  ele- 
vated out  of  its  true  position.  Moreover,  since  on  ac- 
count of  the  continual  increase  of  density  in  descending 
through  the  atmosphere,  the  light  would  be  continually 
turned  out  of  its  course  more  and  more,  it  would  there- 
fore move,  not  in  the  polygon  represented  in  the  figure, 
but  in  a  corresponding  curve,  whose  curvature  is  rapidly 
increased  near  the  surface  of  the  earth. 


68.  What  effect  has  refraction  upon  the  place  of  a  heavenly 
body?  By  what  is  it  occasioned  ?  Illustrate  by  figure  8.  How 
is  a  ray  of  light  affected  by  passing  out  of  a  rarer  into  a  denser 
medium?  Why  is  an  oar  bent  in  the  water  ?  In  what  line 
does  the  light  move  as  it  goes  through  the  atmosphere  ? 


*  The  operation  of  this  principle  is  seen  when  an  oar,  or  any  stick, 
is  thrust  into  water.  As  the  rays  of  light  by  which  the  oar  is  seen,  have 
their  direction  changed  as  they  pass  out  of  water  into  air,  the  apparent 
direction  in  which  the  body  is  seen  is  changed  in  the  same  degree, 
giving  it  a  bent  appearance.  Thus,  in  the  figure,  if  Sax  represents,  the 
oar,  Sab  will  be  the  bent  appearance  as  affected  by  refraction.  The 
transparent  substance  through  which  any  ray  of  light  passes,  is  called 
a  medium.  It  is  a  general  fact  in  optics,  that  when  light  passes  out  of 
a  rarer  into  a  denser  medium,*»s  out  of  air  into  water,  or  out  of  space 
into  air,  it  is  turned  towards  a  perpendicular  to  the  surface  of  the  me- 
dium, and  when  it  passes  out  of  a  denser  into  a  rarer  medium,  as  out 
of  water  into  air,  it  is  turned  from  the  perpendicular.  In  the  above 
ease  the  light,  passing  out  of  space  into  air,  is  turned  towards  the  ra- 
dius of  the  earth,  this  being  perpendicular  to  the  surface  of  the  atmos- 
phere; and  it  is  turned  more  and  more  towards  that  radius  the  nearer 
it  approaches  to  the  earth,  because  the  density  of  the  air  rapidly  in- 
creases. 


40 


THE  EARTH. 


69.  When  a  body  is  in  the  zenith,  since  a  ray  of  light 
from  it  enters  the  atmosphere  at  right  angles  to  the  re- 
fracting medium,  it  suffers  no  refraction.  Consequently, 
the  position  of  the  heavenly  bodies,  when  in  the  zenith, 
is  not  changed  by  refraction,  while,  near  the  horizon, 
where  a  ray  of  light  strikes  the  medium  very  obliquely, 
and  traverses  the  atmosphere  through  its  densest  part, 
the  refraction  is  greatest.  The  following  numbers,  ta- 
ken at  different  altitudes,  will  show  how  rapidly  refrac- 
tion diminishes  from  the  horizorrrrpwards.  The  amount 
of  refraction  at  the  horizon  is  34'  GO7'.  At  different  ele- 
vations it  is  as  follows  : 


Elevation. 

Refraction. 

Elevation. 

Refraction. 

0°   10' 

32'  00" 

30° 

1'  40" 

0°  20' 

30'  00" 

40° 

i'  09" 

1°  00' 

24'  25" 

45° 

0'  58" 

5°  00' 

10'  00" 

60° 

0'  33'' 

10°  00' 

5'  20" 

80° 

0'   10'" 

20°  00' 

2'  39" 

90° 

0'  00" 

From  this  table  it  appears,  that  while  refraction  at  the 
horizon  is  34  minutes,  at  so  small  an  elevation  as  only 
10'  above  the  horizon  it  loses  2  minutes,  more  than  the 
entire  change  from  the  elevation  of  30°  to  the  zenith. 
From  the  horizon  to  1°  above,  the  refraction  is  dimin- 
ished nearly  10  minutes.  The  amount  at  the  horizon, 
at  45°,  and  at  90°,  respectively,  is  34',  58",  and  0.  In 
finding  the  altitude  of  a  heavenly  body,  the  effect  of  pa- 
rallax must  be  added,  but  that  of  refraction  subtracted. 

70.  Since  the  whole  amount  of  refraction  near  the 
horizon  exceeds  33',  and  the  diameters  of  the  sun  and 
moon  are  severally  less  than  this,  these  luminaries  are  in 


69.  Has  refraction  any  effect  on  aflbody  in  the  zenith  ?  Why 
not.  ?  When  is  the  refraction  greatest  ?  What  is  the  amount 
of  refraction  at  the  horizon  ?  Ho\C  much  does  it  lose  within 
10'  of  the  horizon  1  What  is  the  amount  of  refraction  at  an 
elevation  of  45°  ? 


REFRACTION.  41 

view  both  before  they  have  actually  risen  and  after  they 
have  set. 

The  rapid  increase  of  refraction  near  the  horizon,  is 
strikingly  evinced  by  the  oval  figure  which  the  sun  as- 
sumes when  near  the  horizon,  and  which  is  seen  to  the 
greatest  advantage  when  light  clouds  enable  us  to  view 
the  solar  disk.  Were  all  parts  of  the  sun  equally  raised 
by  refraction,  there  would  be  no  change  of  figure  ;  but 
since  the  lower  side  is  more  refracted  than  the  upper, 
the  effect  is  to  shorten  the  vertical  diameter  and  thus  to 
give  the  disk  an  oval  form.  This  effect  is  particularly 
remarkable  when  the  sun,  at  his  rising  or  setting,  is  ob- 
served from  the  top  of  a  mountain,  or  at  an  elevation 
near  the  sea  shore ;  for  in  such  situations  the  rays  of 
light  make  a  greater  angle  than  ordinary,  with  a  perpen- 
dicular to  the  refracting  medium,  and  the  amount  of  re- 
fraction is  proportionally  greater.  In  some  cases  of  this 
kind,  the  shortening  of  the  vertical  diameter  of  the  sun 
has  been  observed  to  amount  to  6',  or  about  one  fifth  of 
the  whole. 

71.  The  apparent  enlargement  of  the  sun  and  moon 
in  the  horizon,  arises  from  an  optical  illusion.  These 
bodies  in  fact  are  not  seen  under  so  great  an  angle  when 
in  the  horizon,  as  when  on  the  meridian,  for  they  are 
nearer  to  us  in  the  latter  case  than  in  the  former.  The 
distance  of  the  sun  is  indeed  so  great  that  it  makes  very 
little  difference  in  his  apparent  diameter,  whether  he  is 
viewed  in  the  horizon  or  on  the  meridian ;  but  with  the 
moon  the  case  is  otherwise  ;  its  angular  diameter,  when 
measured  with  instruments,  is  perceptibly  larger  at  the 
time  of  its  culmination.  Why  then  do  the  sun  and 
moon  appear  so  much  larger  when  near  the  horizon?  It 


70.  What  effect  has  refraction  upon  the  appearances  of  the 
sun  and  moon  when  near  rising  or  setting  1  Explain  the  oval 
figure  of  the  sun  when  near  the  horizon.  In  what  position  of 
the  spectator  does  this  phenomenon  appear  most  conspicuous? 
How  much  has  the  vertical  diameter  of  the  sun  ever  appeared 
to  be  shortened  ? 

4* 


42  THE  EARTH. 

is  owing  to  that  general  law,  explained  in  optics,  by 
which  we  judge  of  the  magnitudes  of  distant  objects, 
not  merely  by  the  angle  they  subtend  at  the  eye,  but 
also  by  our  impressions  respecting  their  distance,  allow- 
ing, under  a  given  angle,  a  greater  magnitude  as  we  im- 
agine the  distance  of  a  body  to  be  greater.  Now,  on  ac- 
count of  the  numerous  objects  usually  in  sight  between 
us  and  the  sun,  when  on  the  horizon,  he  appears  much 
farther  removed  from  us  than  when  on  the  meridian,  and 
ve  assign  to  him  a  proportionally  greater  magnitude.  If 
we  view  the  sun,  in  the  two  positions,  through  smoked 
glass,  no  such  difference  of  size  is  observed,  for  here  no 
objects  are  seen  but  the  sun  himself. 

The  extraordinary  enlargement  of  the  sun  or  moon, 
particularly  the  latter,  when  seen  at  its  rising  through  a 
grove  of  trees,  depends  on  a  different  principle.  Through 
the  various  openings  between  the  trees,  we  see  differ- 
ent images  of*  the  sun  or  moon,  a  great  number  of  which 
overlapping  each  other,  swell  the  dimensions  of  the 
body  under  the  most  favourable  circumstances,  to  a  very 
unusual  size. 

TWILIGHT. 

72.  Twilight  also  is  another  phenomenon  depending 
upon  the  agency  of  the  earth's  atmosphere.  It  is  that 
illumination  of  the  sky  which  takes  place  just  before 
sunrise,  and  which  continues  after  sunset.  It  is  due 
partly  to  refraction  and  partly  to  reflexion,  but  mostly  to 
the  latter.  While  the  sun  is  within  18°  of  the  horizon, 
before  it  rises  or  after  it  sets,  some  portion  of  its  light  is 
conveyed  to  us  by  means  of  numerous  reflections  from 


71.  To  what  is  the  apparent  enlargement  of  the  sun  and 
moon  when  near  the  horizon  owing  ?  Are  these  bodies  seen 
under  a  greater  angle  when  in  the  horizon  than  in  the  zenith  ? 
To  what  general  law  of  optics  is  the  enlargement  to  be  ascri- 
bed ?  How  is  it  when  we  view  the  sun  through  smoked  glass  ? 
To  what  is  the  extraordinary  enlargement  of  these  luminaries 
owing,  when  seen  through  a  grove  of  trees  ? 


the  atmosphere.  Let  AB  (Fig.  9,)  be  the  horizon  of 
the  spectator  at  A,  and  let  SS  be  a  ray  of  light  from  the 
sun  when  it  is  two  or  three  degrees  below  the  horizon. 
Then  to  the  observer  at  A,  the  segment  of  the  atmos- 
phere ABS  would  be  illuminated.  To  a  spectator  at  C, 
whose  horizon  was  CD,  the  small  segment  SDx  wrould 
be  the  twilight ;  while,  at  E,  the  twilight  would  disap- 
pear altogether. 

73.  At  the  equator,  where  the  circles  of  daily  motion 
aie  perpendicular  to  the  horizon,  the  sun  descends 
through  18°  in  an  hour  and  twelve  minutes  (r|-=ljh.), 
and  the  light  of  day  therefore  declines  rapidly,  and  as 
rapidly  advances  after  day  break  in  the  morning.  At  the 
pole,  a  constant  twilight  is  enjoyed  while  the  sun  is 
within  18°  of  the  horizon,  occupying  nearly  two- thirds 
of  the  half  year  when  the  direct  light  of  the  sun  is  with- 
drawn, so  that  the  progress  from  continual  day  to  con- 


72.  Define  twilight — How  many  degrees  below  the  horizon 
is  the  sun  when  it  begins  and  ends  ?     How  is  the  light  of  the 
sun  conveyed  to  us  ?     Explain  by  the  figure. 

73.  What  is  the  length  of  twilight  at  the  equator?     How 
long  does  it  last  at  the  poles  ?     How  is  the  progress  from  con- 
tinual day  to  Constant  night?     To  the  inhabitants  of  an  oblique 
sphere,  in  what  latitudes  is  twilight  longest  ? 


_       44  THE  EARTH. 

stant  night  is  exceedingly  gradual.  To  the  inhabitants 
of  an  oblique  sphere,  the  twilight  is  longer  in  proportion 
as  the  place  is  nearer  the  elevated  pole. 

74.  Were  it  not  for  the  power  the  atmosphere  has  of 
dispersing  the  solar  light,  and  scattering  it  in  various  di- 
rections, no  objects  would  be  visible  to  us  out  of  direct 
sunshine ;  every  shadow  of  a  passing  cloud  would  be 
pitchy  darkness  ;  the  stars  would  be  visible  all  day,  and 
every  apartment  into  which  the  sun  had  not  direct  ad- 
mission, would  be  involved  in  the  obscurity  of  night. 
This  scattering  action  of  the  atmosphere  on  the  solar 
light,  is  greatly  increased  by  the  irregularity  of  tempera- 
ture caused  by  the  sun,  which  throws  the  atmosphere 
into  a  constant  state  of  undulation,  and  by  thus  bringing 
together  masses  of  air  of  different  temperatures,  produces 
partial  reflections  and  refractions  at  their  common  boun- 
daries, by  which  means  much  light  is  turned  aside  from 
the  direct  course,  and  diverted  to  the  purposes  of  general 
illumination.  In  the  upper  regions  of  the  atmosphere, 
as  on  the  tops  of  very  high  mountains,  where  the  air  is 
too  much  rarefied  to  reflect  much  light,  the  sky  assumes 
a  black  appearance,  and  stars  become  visible  in  the  dav 
time. 


CHAPTER   IV. 

OF    TIME. 


75.  TIME  is  a  measured  portion  of  indefinite  duration.* 
The  great  standard  of  time  is  the  period  of  the  revo- 
lution of  the  earth  on  its  axis,  which,  by  the  most  exact 


74.  What  would  happen  were  it  not  for  the  power  the  at- 
mosphere has  of  dispersing  the  solar  light  ?  What  would  every 
shadow  of  a  cloud  produce  ?  How  is  the  scattering  action  of 
the  atmosphere  increased  ?  What  is  the  aspect  of  the  sky  in 
the  upper  regions  of  the  atmosphere-? 

*  From  old  Eternity's  mysterious  orb, 

Was  Time  cut  off  and  cast  beneath  the  skies. — Young- 


TIME.  45 

observations,  is  found  to  be  always  the  same.  The  time 
of  the  earth's  revolution  on  its  axis  is  called  a  sidereal 
day,  and  is  determined  by  the  revolution  of  a  star  from 
the  instant  it  crosses  the  meridian,  until  it  comes  round 
to  the  meridian  again.  '  This  interval  being  called  a  si- 
dereal day,  it  is  divided  into  24  sidereal  hours.  Obser- 
vations taken  upon  numerous  stars,  in  different  ages  of 
the  world,  show  that  they  all  perform  their  diurnal  rev- 
olutions in  the  same  time,  and  that  their  motion  during 
any  part  of  the  revolution  is  perfectly  uniform. 

76.  Solar  time  is  reckoned  by  the  apparent  revolution 
of  the  sun,  from  the  meridian  round  to  the  same  meridian 
again.  Were  the  sun  stationary  in  the  heavens,  like  a 
fixed  star,  the  time  of  its  apparent  revolution  would  be 
equal  to  the  revolution  of  the  earth  on  its  axis,  and  the 
solar  and  the  sidereal  days  would  be  equal.  But  since 
the  sun  passes  from  west  to  east,  through  360°  in  365J 
days,  it  moves  eastward  nearly  1°  a  day,  (59'  8".3). 
While,  therefore,  the  earth  is  turning  round  on  its  axis, 
the  sun  is  moving  in  the  same  direction,  so  that  when 
we  have  come  round  under  the  same  celestial  meridian 
from  which  we  started,  we  do  not  find  the  sun  there, 
but  he  has  moved  eastward  nearly  a  degree,  and  the 
earth  must  perform  so  much  more  than  one  complete 
revolution,  in  order  to  come  under  the  sun  again.  Now 
since  a  place  on  the  earth  gains  359°  in  24  hours,  how 
long  will  it  take  to  gain  1°  ? 

24 
359  :  24  : :  1  :         =^  nearly. 


75.  Define  time — What  is  the  standard  of  time  ?     What  is 
a  sidereal  day  ?     Do  the  stars  all  perform  their  revolutions  in 
the  same  time  ?     Is  their  motion  uniform  1^ 

76.  How  is  the  solar  time  reckoned?  How  far  does  the  sun 
move  eastward  in  a  day  ?  How  much  longer  is  the  solar  than  the 
sidereal  day  ?     If  we  reckoned  the  sidereal  day  24  hours,  how 
should  we  reckon  the  solar?     Reckoning  the  solar  day  at  24 
hours,  how  long  is  the  sidereal  ? 


46  THE  EARTH. 

Hence  the  solar  day  is  about  4  minutes  longer  than 
the  sidereal ;  and  if  we  were  to  reckon  the  sidereal  day 
24  hours,  we  should -reckon  the  solar  day  24h.  4m.  To 
suit  the  purposes  of  society  at  large,  however,  it  is  found 
most  convenient  to  reckon  the  solar  day  24  hours,  and  to 
throw  the  fraction  into  the  sidereal  day.  Then, 

24h  4m.  :  24  : :  24  :  23h.  56m.  nearly  (23h.  56m  4*.09) 
rrthe  length  of  a  sidereal  day. 

77.  The  solar  days,  however,  do  not  always  differ  from 
the  sidereal  by  precisely  the  same  fraction,  since  the  in- 
crements of  right  ascension,  which  measure  the  differ- 
ence between  a  sidereal  and  a  solar  day,  are  not  equal  to 
each  other.     Apparent  time,  is  time  reckoned  by  the 
revolutions  of  the  sun  from  the  meridian  to  the  meridian 
again.      These  intervals  being  unequal,  of  course  the 
apparent  solar  days  are  unequal  to  each  other. 

78.  Mean   time,  is   time   reckoned   by   the   average 
length  of  all  the  solar  days  throughout  the  year.     This 
is  the  period  which  constitutes  the  civil  day  of  24  hours, 
beginning  when  the  sun  is  on  the  lower  meridian,  name- 
ly, at  12  o'clock  at  night,  and  counted  by  12  hours  from 
the  lower  to  the  upper  culmination,  and  from  the  upper 
to  the  lower.     The  astronomical  day  is  the  apparent  so- 
lar day  counted  through  the  whole  24  hours,  instead  of 
by  periods  of  12  hours  each,  and  begins  at  noon.     Thus 

10  days  and  14  hours  of  astronomical  time,  would  be 

1 1  days  and  2  hours  of  apparent  time  ;  for  when  the  10th 
astronomical  day  begins,  it  is  10  days  and  12  hours  of 
civil  time. 

79.  Clocks  are  usually  regulated  so  as  to  indicate  mean 
solar  time  ;  yet  as  this  is  an  artificial  period,  not  marked 


77.  Do  the  solar  days  always  differ  from  the  sidereal  by  the 
same  quantity  ?     Define  apparent  time. 

78.  Define   mean  time.     What  constitutes  the  civil  day  ? 
What  makes  an  astronomical  day  ?     When  does  the  civil  day 
begin  ?     When  does  the  astronomical  day  begin  ? 


THE  CALENDAR.  47 

off,  like  the  sidereal  day,  by  any  natural  event,  it  is  ne- 
cessary to  know  how  much  is  to  be  added  to  or  sub- 
tracted from  the  apparent  solar  time,  in  order  to  give  the 
corresponding  mean  time.  The  interval  by  which  ap- 
parent time  differs  from  mean  time,  is  called  the  equation 
of  time.  If  a  clock  were  constructed  (as  it  may  be)  so 
as  to  keep  exactly  with  the  sun,  going  faster  or  slower 
according  as  the  increments  of  right  ascension  were 
greater  or  smaller,  and  another  clock  were  regulated  to 
mean  time,  then  the  difference  of  the  two  clocks,  at  any 
period,  would  be  the  equation  of  time  for  that  moment. 
If  the  apparent  clock  were  faster  than  the  mean,  then 
the  equation  of  time  must  be  subtracted  ;  but  if  the  ap- 
parent clock  were  slower  than  the  mean,  then  the  equa- 
tion of  time  must  be  added,  to  give  the  mean  time. 
The  two  clocks  would  differ  most  about  the  3d  of  No- 
vember, when  the  apparent  time  is  16Tm  greater  than  the 
mean  (16m  16S.7).  But,  since  apparent  time  is  some- 
times greater  and  sometimes  less  than  mean  time,  the 
two  must  obviously  be  sometimes  equal  to  each  other. 
This  is  in  fact  the  case  four  times  a  year,  namely,  April 
15th,  June  15th,  September  1st,  and  December  24th. 

THE  CALENDAR. 

80.  The  astronomical  year  is  the  time  in  which  the 
sun  makes  one  revolution  in  the  ecliptic,  and  consists  of 
365d.  5h.  48m.  51s  60.  The  civil  year  consists  of  365 
days.  The  difference  is  nearly  6  hours,  making  one  day 
in  four  years. 

The  most  ancient  nations  determined  the  number  of 
days  in  the  year  by  means  of  the  stylus,  a  perpendicular 


79  What  time  do  clocks  commonly  keep  j  Define  the  equa- 
tion of  time.  How  might  two  clocks  be  regulated  so  that  their 
difference  would  indicate  the  equation  of  time  1  How  must 
the  equation  of  time  be  applied  when  the  apparent  clock  is 
faster  than  the  mean  1  How  when  it  is  slower  ?  When  would 
the  two  clocks  differ  most  ?  How  much  would  they  then  differ7 
When  would  they  come  together  ? 


48  THE  EARTH. 

rod  which  casts  its  shadow  on  a  smooth  plane,  bearing  a 
meridian  line.  The  time  when  the  shadow  was  shortest, 
would  indicate  the  day  of  the  summer  solstice ;  and  the 
number  of  days  which  elapsed  until  the  shadow  returned 
to  the  same  length  again,  would  show  the  number  of 
days  in  the  year.  This  was  found  to  be  365  wnc  ie 
days,  and  accordingly  this  period  was  adopted  for  trie 
civil  year.  Such  a  difference,  however,  between  the 
civil  and  astronomical  years,  at  length  threw  all  dates 
into  confusion.  For,  if  at  first  the  summer  solstice  hap- 
pened on  the  21st  of  June,  at  the  end  of  four  years,  the 
sun  would  not  have  reached  the  solstice  until  the  22d  of 
June,  that  is,  it  would  have  been  behind  its  time.  At 
the  end  of  the  next  four  years  the  solstice  would  fall  on 
the  23d ;  and  in  process  of  time  it  would  fall  succes- 
sively on  every  day  of  the  year.  The  same  would  be 
true  of  any  other  fixed  date.  Julius  Caesar  made  the 
first  correction  of  the  calendar,  by  introducing  an  inter- 
calary day  every  fourth  year,  making  February  to  con- 
sist of  29  instead  of  28  days,  and  of  course  the  whole 
year  to  consist  of  366  days.  This  fourth  year  was  de- 
nominated Bissextile.  It  is  also  called  Leap  Year. 

8],  But  the  true  correction  was  not  6  hours,  but  5h 
49m. ;  hence  the  intercalation  was  too  great  by  1 1  min- 
utes. This  small  fraction  would  amount  in  100  years 
to  f  of  a  day,  and  in  1000  years  to  more  than  7  days. 
From  the  year  325  to  1582,  it  had  in  fact  amounted  to 
about  10  days  ;  for  it  was  known  that  in  325,  the  vernal 
equinox  fell  on  the  21st  of  March,  whereas,  in  1582  it 
fell  on  the  llth.  In  order  to  restore  the  equinox  to  the 
same  date,  Pope  Gregory  XIII,  decreed,  that  the  year 


80.  Define  the  astronomical  year — What  is  its  exact  period? 
Of  how  many  days  does  the  civil  year  consist?  How  much 
shorter  is  the  civil  than  the  astronomical  year  ?  How  didthe  most 
ancient  nations  determine  the  number  of  days  in  the  year  ? 
When  would  the  stylus  mark  the  shortest  day  and  when  the 
longest  ?  Explain  the  confusion  which  arose  by  reckoning  the 
year  only  365  days.  How  did  Julius  Csesar  reform  the  calendar  ? 


THE  CALENDAR  49 

should  be  brought  forward  10  days,  by  reckoning  the 
5th  of  October  the  15th.  In  order  to  prevent  the  cal- 
endar from  falling  into  confusion  afterwards,  the  follow- 
ing rule  was  adopted : 

Every  year  whose'  number  is  not  divisible  by  4  with' 
cut  a  remainder,  consists  of  365  days  ;  every*year  which 
is  so  divisible,  but  is  not  divisible  by  100,  of  366;  every 
year  divisible  by  100  but  not  by  400,  again  of  365;  and 
every  year  divisible  by  400,  of  366. 

Thus  the  year  1838,  not  being  divisible  by  4,  contains 
365  days,  while  1836  and  1840  are  leap  years.  Yet  to 
make  every  fourth  year  consist  of  366  days  would  in- 
crease it  too  much  by  about  f  of  a  day  in  100  years ; 
therefore  every  hundredth  year  has  only  365  days. 
Thus  1800,  although  divisible  by  4  was  not  a  leap  year, 
but  a  common  year.  But  we  have  allowed  a  whole  day 
in  a  hundred  years,  whereas  we  ought  to  have  allowed 
only  three  fourths  of  a  day.  Hence,  in  400  years  we 
should  allow  a  day  too  much,  and  therefore  we  let  the 
400th  year  remain  a  leap  year.  This  rule  involves  an 
error  of  less  than  a  day  in  4237  years.  If  the  rule  were 
extended  by  making  every  year  divisible  by  4000  (which 
would  now  consist  of  366  days)  to  consist  of  365  days, 
the  error  would  not  be  more  than  one  day  in  100,000 
years. 

82.  This  reformation  of  the  calendar  was  not  adopted 
in  England  until  1752,  by  which  time  the  error  in  the 
Julian  calendar  amounted  to  about  11  days.  The  year 
was  brought  forward,  by  reckoning  the  3d  of  September 
the  14th.  Previous  to  that  time  the  year  began  the  25th 


81.  By  how  many  minutes  was  the  allowance  made  by  the 
Julian  calendar  too  great  ?  To  how  much  would  the  error 
amount  in  one  hundred  years  ?  To  how  much  in  a  thousand 
years  ?  To  how  much  had  it  amounted  from  the  year  325  to 
1582  ?  What  changes  did  Pope  Gregory  make  in  the  year? 
State  the  rule  for  the  calendar.  Of  the  three  years  1836, 
1 838,  and  1 840,  which  are  leap  years  ?  Was  1 800  a  leap  year  ? 
How  is  every  400th  year  ? 

5 


50  THE  EARTH. 

of  March  ;  but  it  was  now  made  to  begin  on  the  1st  of 
January,  thus  shortening  the  preceding  year,  1751,  one 
quarter.* 

As  in  the  year.  1582,  the  error  in  the  Julian  calendar 
amounted^to  10  days,  and  increased  by  f  of  a  day  in  a 
century,  a*t  present  the  correction  is  12  days  ;  and  the 
number  of  the  year  w;1l  differ  by  one  with  respect  to 
dates  between  the  1st  of  January  and  the  25th  of  March, 

Examples.  General  Washington  was  born  Feb.  11 
1781,  old  style  ;  to  what  date  does  this  correspond  in 
new  style  ? 

As  the  date  is  the  earlier  part  of  the  18th  century,  the 
correction  is  1 1  days,  which  makes  the  birth  day  fall  on 
the  22d  of  February ;  and  since  the  year  1731  closed 
the  25th  of  March,  while  according  to  new  style  1732 
would  have  commenced  on  the  preceding  1st  of  Janu- 
ary ;  therefore,  the  time  required  is  Feb.  22,  1732.  It 
is  usual,  in  such  cases,  to  write  both  years,  thus  :  Feb. 
11,  1731-2,  O.  S. 

2.  A  great  eclipse  of  the  sun  happened  May  15th, 
1836  ;  to  what  date  would  this  time  correspond  in  old 
style  ?  Ans.  May  3d. 

83.  The  common  year  begins  and  ends  on  the  same 
day  of  the  week  ;  but  leap  year  ends  one  day  later  in  the 
week  than  it  began. 

For  52x7=364  days;  if  therefore  the  year  begins 
on  Tuesday,  for  example,  364  days  would  complete  52 
weeks,  and  one  day  would  be  left  to  begin  another  week, 


82.  When  was  this  reformation  first  adopted  in  England  ? 
How  was  the  year  brought  forward  ?  When  did  the  year  be- 
gin before  that  time  ?  To  how  many  days  did  the  error  amount 
in  1752  ?  How  many  days  are  allowed  at  present  between 
old  and  new  style  ? 


*  Russia,  and  the  Greek  Church  generally,  adhere  to  the  old  style. 
[n  order  to  make  the  Russian  dates  correspond  to  ours,  we  must  add  to 
them  12  days.  France  and  other  Catholic  countries,  adopted  the  Gre- 
gorian calendar  soon  after  it  was  promulgated 


ASTRONOMICAL   INSTRUMENTS  51 

and  the  following  year  would  begin  on  Wednesday. 
Hence,  any  day  of  the  month  is  one  day  later  in  the 
week  than  the  corresponding  day  of  the  preceding  year. 
Thus,  if  the  16th  of  November,  1838,  falls  on  Friday, 
the  Itith  of  November,  1837,  fell  on  Thursday,  and  in 
1839  will  fall  on  Saturday.  But  if  leap  year  begins  on 
Sunday,  it  ends  on  Monday,  and  the  following  year  be- 
gins on  Tuesday ;  while  any  given  day  of  the  month  is 
two  days  latei  in  the  week  than  the  corresponding  date 
of  the  preceding  year. 


CHAPTER    V. 

OF  ASTRONOMICAL  INSTRUMENTS FIGURE  AND  DENSITY  OP 

THE  EARTH. 

84.  THE  most  ancient  astronomers  employed  no  in- 
struments of  observation,  but  acquired  their  knowledge 
of  the  heavenly  bodies  by  long  continued  and  most  at- 
tentive inspection  with  the  naked  eye.    Instruments  for 
measuring  angles  were  first  used  in  the  Alexandrian 
school,  about  300  years  before  the  Christian  era, 

85.  Wherever  we  are  situated  on  the  earth  we  appear 
to  be  in.  the  center  of  a  vast  sphere,  on  the  concave  sur- 
face of  which  all  celestial  objects  are  inscribed.     If  we 
take  any  two  points  on  the  surface  of  the  sphere,  as  two 
stars  for  example,  and  imagine  straight  lines  to  be  drawn 
to  them  from  the  eye,  the  angle  included  between  these 


w 

83.  If  the  common  year  begins  on  a  certain  day  of  the  week, 
how  will  it  end  ?      How  is  it  with  leap  year  1     How  does  any 
day  of  the  month  compare  in  the  preceding  and  following  year 
with  respect  to  the  day  of  the   week  ?     How  is   this  in  leap 
year? 

84.  How  did  the  most  ancient  nations  acquire  their  knowl- 
edge of  the  heavenly  bodies  ?     When  were  astronomical  in- 
struments first  introduced  ? 


52  THE  EARTH. 

lines  will  be  measured  by  the  arc  of  the  sky  contained 
between  the  two  points.     Thus  if  HBD,  (Fig.  10,)  rep- 
Fig.  10. 


resents  the  concave  surface  of  the  sphere,  A,  B,  two 
points  on  it,  as  two  stars,  and  CA,  CB,  straight  lines 
drawn  from  the  spectator  to  those  points,  then  the  angu- 
lar distance  between  them  is  measured  by  the  arc  AB, 
or  the  angle  ACB.  But  this  angle  may  be  measured  on 
a  much  smaller  circle,  having  the  same  center,  as  EFG, 
since  the  arc  EF  will  have  the  same  number  of  degrees 
as  the  arc  AB.  The  simplest  mode  of  taking  an  angle 
between  two  stars,  is  by  means  of  an  arm  opening  at  a 
joint  like  the  blade  of  a  penknife,  the  end  of  the  arm 
moving  like  CE  upon  the  graduated  circle  KEG. 

The  common  surveyor's  compass  affords  a  simple  ex- 
ample of  angular  measurement.  Here  the  needle  lies  in 
a  north  and  south  line,  while  the  circular  rim  of  the 
compass.,  when  the  instrument  is  level,  corresponds  to 
the  horizon.  Hence  the  compass  shows  how  many  de- 
grees any  object  to  which  we  direct  the  eye,  lies  east  or 
\vest  of  the  meridian. 


85.  How  is  the  angular  distance  between  two  points  on  the 
celestial  sphere  measured  ?  Explain  figure  10,  Show  how  the 
circles  of  the  sphere  may  be  truly  represented  by  the  smaller 
circles  of  the  instrument,  as  the  horizon  by  the  surveyor's  com- 
pass. Explain  the  simplest  mode  of  taking  angles  by  figure  10 


ASTRONOMICAL  INSTRUMENTS.  53 

86.  It  is  obvious  that  the  larger  the  graduated  circle 
is,  the  more  minutely  its  limb  may  be  divided.     If  the 
circle  is  one  foot  in  diameter,  each  degree  will  occupy 
jL  of  an  inch.     If  the  circle   is  20   feet  in  (diameter,  a 
degree  will  occupy  the  space  of  two  inches  and  could 
be  easily  divided  to  minutes,  since  each  minute  would 
cover  a  space  of  ^  of  an  inch.     Refined  astronomical 
circles  are  now  divided  with  very  great  skill  and  accu-- 
racy,  the  spaces  between  the  divisions  being,  when  read 
off,  magnified  by  a  microscope  ;  but  in  former  times, 
astronomers  had  no  mode  of  measuring  small  angles 
but  by  employing  very  large  circles.     But  the  telescope 
and  microscope  enable  us  at  present  to  measure  celestial 
arcs  much  more  accurately  than  was  done  by  the  older 
astronomers.  *  t 

The  principal  instruments  employed  in  astronomy, 
are  the  Telescope,  the  Transit  Instrument,  the  Altitude 
and  Azimuth  Instrument,  and  the  Sextant. 

87.  The   Telescope  has  greatly  enlarged  our  knowl- 
edge of  astronomy,  both  by  revealing  to  us  many  things 
invisible  to  the  naked  eye,  and  also  by  enabling  us  to 
attain  a  much  higher  degree  of  accuracy  than  we  could 
otherwise  reach,  in  angular  measurements.     It  was  in- 
vented by  Galileo  about  the  year  1600.     The  powers  of 
the  telescope  were  improved  and  enlarged  by  successive 
efforts,  and  finally,  about  50  years  ago,  telescopes  were 
constructed  in  England  by  Dr.  Herschel,  of  a  size  and 
power  that  have  not  since  been  surpassed. 

A  complete  knowledge  of  the  telescope  cannot  be  ac- 
quired without  an  acquaintance  with  the  science  of  op- 
tics ;  but  we  may  perhaps  convey  to  one  unacquainted 
with  that  science,  some  idea  of  the  leading  principles  of 


86.  What  is  the  advantage  of  having  large  circles  for  angu- 
lar measurements  ?  When  the  circle  is  one  foot  in  diameter, 
what  space  will  1  °  occupy  on  the  limb  ?  What  space  when 
the  circle  is  twenty  feet  in  diameter  ?  What  are  the  princi- 
pal instruments  used  in  astronomical  observations  ? 


54  THE  EARTH. 

this  noble  instrument.  By  means  of  the  telescope,  we 
first  form  an  image  of  a  distant  object  as  the  moon  for 
example,  and  then  magnify  that  image  by  a  microscope. 
Let  us  first  see  how  the  image  is  formed.  This  may  be 
done  either  by  a  convex  lens,  or  by  a  concave  mirror.  A 
convex  lens  is  a  flat  piece  of  glass,  having  its  two  faces 
convex,  or  spherical,  as  is  seen  in  a  common  sun  glass. 
Every  one  who  has  seen  a  sun  glass,  knows  that  when 
held  towards  the  sun  it  collects  the  solar  rays  into  a 
small  bright  circle  in  the  focus.  This  is  in  fact  a  small 
image  of  the  sun.  In  the  same  manner  the  image  •  of 
any  distant  object,  as  a  star,  may  be  formed  as  is  repre- 
sented in  the  following  diagram.  Let  ABCD  represent 
Fig.  11. 


the  tube  of  a  telescope.  At  the  front  end,  or  at  the  end 
which  is  directed  towards  the  object,  (which  we  will 
suppose  to  be  the  moon,)  is  inserted  a  convex  lens, 
L,  which  receives  the  rays  of  light  from  the  moon,  and 
collects  them  into  the  focus  at  a,  forming  an  image  of 
the  moon.  This  image  is  viewed  by  a  magnifier  attach- 
ed to  the  end  BC.  The  lens  L  is  called  the  object-glass, 
and  the  microscope  in  BC  the  eye-glass.  We  apply  a 
magnifier  to  this  image  just  as  we  would  to  any  object ; 


87.  Who  invented  the  telescope  ?  Who  constructed  tele- 
scopes of  great  size  and  power?  Explain  the  leading  prin- 
ciple of  the  telescope.  How  is  the  image  formed  1  What  is 
a  convex  lens  ?  How  does  it  affect  parallel  rays  of  light  ? 
How  do  we  view  the  image  formed  by  the  lens  ?  How  is  the 
image  magnified  ?  How  is  it  rendered  brighter  ? 


ASTRONOMICAL  INSTRUMENTS.  5^ 

ncTby  greatly  enlarging  its  dimensions,  we  may  render 
us  various  parts  far  more  distinct  than  they  would  other- 
wise be,  while  at  the  same  time  the  object  lens  collects 
and  conveys  to  the^eye  a  much  greater  quantity  of  light 
than  would  proceed  directly  from  the  body  under  exam- 
ination. A  very  small  beam  of  light  only  from  a  distant 
object,  as  a  star,  can  enter  the  eye  directly ;  but  a  lens 
one  foot  in  diameter  will  collect  a  beam  of  light  of  the 
same  dimensions,  and  convey  it  to  the  eye.  By  these 
means  many  obscure  celestial  objects  become  distinctly 
visible,  which  would  otherwise  be  either  too  minute,  or 
not  sufficiently  luminous  to  be  seen  by  us. 

88.  But  the  image  may  also  be  formed  by  means  of  a 
concave  mirror,  which,  as  well  as  the  convex  lens,  has 
the  property  of  collecting  the  rays  of  light  which  pro- 
ceed from  any  luminous  body,  and  of  forming  an  image 
of  that  body.  The  image  formed  by  the  concave  mir- 
ror is  magnified  by  a  microscope  in  the  same  manner  as 
when  formed  by  the  convex  lens.  When  the  lens  is 
used  to  form  an  image,  the  instrument  is  called  a  Re- 
fracting telescope  ;  when  a  concave  mirror  is  used,  it  is 
called  a  Reflecting  telescope. 

The  telescope  in  its  simplest  form  is  employed  not  so 
much  for  angular  measurements,  as  for  aiding  the  pow- 
ers of  vision  in  viewing  the  celestial  bodies.  When  di- 
rected to  the  sun,  it  reveals  to  us  various  irregularities  on 
his  disk  not  discernible  by  naked  vision  ;  when  turned 
upon  the  moon  or  the  planets,  it  affords  us  new  and  in- 
teresting views,  and  enables  us  to  see  in  them  the  linea- 
ments of  other  worlds  ;  and  when  brought  to  bear  upon 
the  fixed  stars,  it  vastly  increases  their  number  and  re- 
veals to  us  many  surprising  facts  respecting  them. 


88.  How  is  an  image  formed  by  a  concave  mirror?  How  is 
this  image  magnified?  *When-is  the  instrument  called  a  re- 
fracting and  when  a  reflecting  telescope  ?  For  what  pur- 
poses are  telescopes  chiefly  employed  ? 


56 


THE  EARTH. 


89.  The  Transit  Instrument  is  a  telescope,  which  is 
fixed  permanently  in  the  meridian,  and  moves  only  in 
that  plane.  It  rests  on  a  horizontal  axis,  which  consists 
gf  two  hollow  cones  applied  base  to»base,  a  form  uniting 
lightness  and  strength.  The  two  ends  of  the  axis  rest 
Fig.  12. 


on  two  firm  supports,  as  pillars  of  stone,  for  example,  so 
connected  with  the  building  as  to  be  as  free  as  possible 
from  all  agitation.  In  figure  12,  AD  represents  the  tele- 


89.  What  is  a  Transit  Instrument  ?  On  what  supports  does 
it  rest  as  represented  in  figure  12.  Whv  are  they  made  so  firm? 
Describe  all  parts  of  the  instrument,  what  is  its  use  ?  How 
used  to  regulate  clocks  and  watches  ?  What  kind  of  time  is 
shown  when  the  sun  is  on  the  meridian  ?  How  is  this 
verted  into  mean  t'me  ?  Give  an  example. 


cori- 


ASTRONOMICAL  INSTRUMENTS.  57 

scope,  E,  W,  massive  stone  pillars  supporting  the  hori 
zontal  axis,  beneath  which  is  seen  a  spirit  level,  (which 
is  used  to  bring  the  axis  to  a  horizontal  position,)  and  n 
a  vertical  circle  graduated  N  into  degrees  and  minutes. 
This  circle  serves  the  purpose  of  placing  the  instrument 
at  any  required  altitude,  or  distance  from  the  zenith,  and 
of  course  for  determining  altitudes  and  zenith  distances. 
The  use  of  the  transit  instrument  is  to  show  the  pre- 
cise moment  when  a  heavenly  body  is  on  the  meridian. 
One  of  its  uses  is  to  enable  us  to  obtain  the  true  time, 
and  thus  to  regulate  our  clocks  and  watches.  We  find 
when  the  sun's  center  is  on  the  meridian,  and  this  gives 
us  the  time  of  noon  or  apparent  time.  (Art.  78.)  But 
watches  and  clocks  usually  keep  mean  time,  and  there- 
fore in  order  to  set  our  time  piece  by  the  transit  instru- 
ment, we  must  apply  the  equation  of  time. 


90.  A  TiooTi  mark  may  easily  be  made  by  the  aid  of 
the  Transit  Instrument.  A  window  sill  is  frequently 
selected  as  a  suitable  place  for  the  mark,  advantage  be- 
ing taken  of  the  shadow  projected  upon  it  by  the  per- 
pendicular casing  of  the  window.  Let  an  assistant  stand 
with  a  rule  laid  on  the  line  of  shadow  and  with  a  knife 
ready  to  make  the  mark,  the  instant  when  the  observer 
at  the  Transit  Instrument  announces  that  the  center  of 
the  sun  is  on  the  meridian.  By  a  concerted  signal,  as 
the  stroke  of  a  bell,  the  inhabitants  of  a  town  may  all 
fix  a  noon  mark  from  the  same  observation.  It  must  be 
borne  in  mind,  however,  that  the  noon  mark  gives  the 
apparent  time,  and  that  the  equation  of  time  must  be 
allowed  for  in  setting  the  clock  or  watch.  Suppose  we 
wish  to  set  our  clock  right  on  the  first  of  January.  We 
find  by  a  table  of  the  equation  of  time,  that  mean  time 
then  precedes  apparent  time  3m.  43s.  ;  we  must  there- 
fore set  the  clock  at  3m.  43s.  the  instant  tfte  center  of 
the  sun  is  on  the  meridian.  If  the  time  had  been  the 
first  of  May  instead  of  the  first  of  January,  then  we 
find  by  the  table  that  3m.  is  to  be  subtracted  from  the 
apparent  time,  and  consequently,  when  the  center  of  the 

90    Describe  the  mode  of  making  a  noon  mark. 


58  THE  EARTH. 

sun  was  on  the  meridian,  we  should  set  our  clock  at  llh. 
57m.  or  3m.  before  twelve. 

91.  The  equation  of  time  varies  a  little  with  different 
years,  but  the  following  table  will  always  be  found 
\vithin  a  few  seconds  of  the  truth.  The  equation  for 
the  current  year  is  given -exactly  in  the  American  Al- 
manac. 

Equation  of  Time  for  Apparent  Noon. 


• 

1 

JAN. 

FEB. 

MAR.JArR. 

MAY 
Sub. 

JUN. 

SnbT 

M.  S 

JUL. 

AUG 

SEPT 

OCT. 

Nov. 

D      1 

Sub. 

Add. 

Add. 

Add. 

Add. 

Add. 

M.  S. 

Add. 

M.  S. 

Add. 

Sub. 

Sub. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

C3 
?> 
4 
5 
(5 

8 
9 
10 

3.43;13.53 
4.1114.  1 
4.3914.  8 
5.  714.14 
5.3414.19 

12.42 
12.30 
12.18 
12.  5 
11.51 

4.  6 
3.48 
3.30 
3.12 
2.54 

3.  0 
3.  7 
3.15 
3.21 
3.27 

2.38 
2.29 
2.19 
2.10 
2.  0 
1.49 
1.39 
1.28 
1.17 
1.  5 

3.19 
3.31 
3.4-2 
3.53 
4.  4 
4.15 
4.25 
4.34 
4.44 
4.53 

5^59 
555 
5.50 
5.45 
5.39 
5.33 
5.25 
5.18 
5..  9 

aO.   I 

sO.17 
0.36 
0.56 
1.15 

10.  9 
10.28 
10.47 
11.  6 
11.24 

16.15 
16.16 
16.17 
16.17 
16.16 

10.54 
10.32 
10.  8 
9.45 
9.20 

6.  1 
6.27 
6.53 

7.18 
7.43 

14.24 
14.27 
14.30 
14.32 
14.33 

11.38 
11.23 
11.  8 
10.53 
10.38 

2.37 
2.19 
2.  2 
1.45 

1.28 

3.32 
3.37 
3.42 
3.46 
3.49 

1.35 
1.55 
2.15 
2.36 
2.56 

11.4216.14 
11.59116.11 
12.1616.  7 
12.33116.  3 
12.49  15.58 

8.55 
8.30 
8.  4 
7.37 
7.10 

LI 
1-3 

13 
11 

if) 

16 

17 
IS 
19 
:30 
-31 
•:2 

•2:! 

-21 
85 

8.  7 
8.31 
8.54 
9.16 
9.37 

14.34 
14.33 
14.32 
14.30 
14.28 

10.22 
10.  6 
9.49 
9.32 
9.15 

1.11 
0.55 
0.39 
0.23 
0.  8 

3.51 
3.53 
3.55 
3.56 
3.56 

0.53 
0.41 
0.29 
0.17 
0.  4 

5.  1 
5.  9 
5.17 
5.24 
5.30 

5.  1 
4.51 
4.41 
4.31 
4.20 

3.17 
3.38 
3.59 
4.20 
4.41 

13.  515.51 
13.20  15.44 
13.34  15.37 
I3.49jl5.28 
14.  215.18 

6.43 
6.15 
5.47 
5.18 
4.49 

9.58 
10.19 
10.38 
10.57 
11.15 
11.33 
11.49 
12.  5 
12.20 
1235 
12.48 
13.  1 
13.13 
13.24 
13.35 
1344 

14.25 
14.20 
14.16 
14.10 
14.  4 

8.58 
8.41 

8.23 
8.  5 

7.47 

Sub. 

0.  7 
0.22 
0.36 
0.50 
1.  3 
1.16 
1.29 
1.41 
152 
2.  4 
2.14 
2.24 
2.34 
2.43 
2.52 

3.56 
3.55 
3.54 
3.52 
3.49 
3~46 
3.42 
3.38 
3.33 
3.28 
3^22 
3.16 
3.  9 
3.  2 
254 
2~46 

Add. 
0/8 
0.21 
0.34 
0,17 
1.0 
1.13 
1.26 
1.39 
1.52 
2.  5 
2.18 
2.30 
2.43 
2.55« 
3.  8j 
"1 

5.37 
5.42 

5.48 
5.52 
557 

0 
6.  3 
6.  (i 
6.  8 
6.  9 

4.  8 
3.56 
3.44 
3.31 
3.17 
3.  3 
2.19 
2.34 
2.19 
2.  3 

L47 
1.30 
1.13 
0.56 

0.38 
0.20 

5.  2 
N5.23 
5.44 
6.  5 
6.26 

«... 

14.28 
14.39 
14.51 
15.  1 

15.  8 
14.56 
14.44 
14.31 
14.17 
1473 
13.47 
13.31 
13.14 
12.56 

4.20 
3.50 
3.21 
2.51 
2.21 

13.58 
13.50 
13.42 
13.34 
13.25 

7.29 
7.11 
6.52 
6.34 
615 

6.4715.11 
7.  815.21 
"7.29^15.29 
7.49  15.37 
8.1015.44: 

1.51 
1.21 
0.51 
0.21 
aO.  9 

-2C, 
37 
28 
29 
30 
ffl 

13.15 
13.  4 
12.54 

5.57 
5.38 
5.20 

5.  ^ 

4.43 

6.10 
6.10 
6.10 
6.  9 

6.  8 
6.  5| 

8.3015.51  12.38 
8.5015.5712.18 
9.11  16.  2fll.58 
9.3016.  611.38 
9.5016.1011.16 

0.39 
1.  9 
1.39 
2.  8 
2.37 

4.25 

116.13! 

3.  6 

91.  Is  the  equation  of  time  the  same  or  different  in  different 
years  ?  In  what  book  mav  it  he  found  exactly  for  the  cur- 
rent year  ? 


ASTRONOMICAL  INSTRUMENTS.  59 

92.  The  Astronomical  Clock  is  the  constant  compan- 
ion of  the  Transit  Instrument.     This  clock  is  so  regu- 
lated as  to  keep  exact  pace  with  the  stars,  and  of  course 
with  the  revolution  of  the  earth  on  its  axis  ;  that  is,  it 
is  regulated  to  sidereal  time.     It  measures  the  progress 
of  a  star,  indicating  an  hour  for  every  15°,  and  24  hours 
for  the  whole  period  of  the  revolution  of  the  star.     Si- 
dereal time,  it  will  be  recollected,  commences  when  the 
vernal  equinox  is  on  the  meridian,  just  as  solar  time  com- 
mences when  the  sun  is  on  the  meridian.     Hence,  the 
hour  by  the  sidereal  clock  has  no  correspondence  with 
the  hour  of  the  day,  but  simply  indicates  how  long  it  is 
since  the  equinoctial  point  crossed  the  meridian.     For 
example,  the  clock  of  an  observatory  points  to  3h  20m. ; 
this  may  be  jn  the  morning,  at  noon,  or  any  other  time 
of  the  day,  since  it  merely  shows  that  it  is  3h.  20m. 
since  the  equinox  was  on  the  meridian.     Hence,  when 
a  star  is  on  the  meridian,  the  clock  itself  shows  its  right 
ascension ;  (Art.  24,)  and  the  interval  of  time  between 
the  arrival  of  any  two  stars  upon  the  meridian,  is  the 
measure  of  their  difference  of  right  ascension. 

93.  Astronomical  clocks  are  made  of  the  best  work- 
manship, with  a  compensation  pendulum,  and   every 
other  advantage  which  can  promote   their  regularity. 
The  Transit  Instrument  itself,  when  once  accurately 
placed  in  the  meridian,  affords  the  means  of  testing  the 
correctness  of  the  clock,  since  one  revolution  of  a  star 
from  the  meridian  to  the  meridian  again,  ought  to  cor- 
respond to  exactly  24  hours  by  the  clock,  and  to  con- 


92.  How  is  the  astronomical  clock  regulated  ?     What  does 
it  measure  ?     How  inany^  degrees  does  a  star  pass  over  in  an 
hour  ?     When  does  sidereal  time  commence  ?     What  is  de- 
noted by  the  hour  and  minute  of  a  sidereal  clock  ?     How  do 
we  determine  the  right  ascension  of  a  star  ? 

93.  How  is  the  workmanship  of  astronomical  clocks?    How 
is  the  correctness  of   a  clock  tested  ?     To   what  degree  of 
perfection   are   clocks  brought  ?      By   what  instrument   are 
clocks  regulated? 


60  THE  EARTH. 

tinue  the  same  from  day  to  day;  and  the  right  asce-j 
sion  of  \arious  stars  as  they  cross  the  meridian,  ought 
to  be  such  by  the  clock  as  they  are  given  in  the  tables, 
where  they  are  stated  according  to  the  accurate  determi- 
nations of  astronomers.  Or  by  taking  ^the  difference  of 
right  ascension  of  any  two  stars  on  successive  days,  it 
will  be  seen  whether  the  going  of  the  clock  is  uniform 
for  that  part  of  the  day  ;  and  by  taking  the  right  ascen- 
sion of  different  pairs  of  stars,  we  may  learn  the  rate  of 
the  clock  at  various  parts  of  the  day.  We  thus  learn, 
not  only  whether  the  clock  accurately  measures  the 
length  of  the  sidereal  day,  but  also  whether  it  goes  uni- 
formly from  hour  to  hour. 

Although  astronomical  clocks  have  been  brought  to  a 
great  degree  of  perfection,  so  as  to  vary  hardly  a  second 
for  many  months,  yet  none  are  absolutely  perfect,  and 
most  are  so  far  from  it  as  to  require  to  be  corrected  by 
means  of  the  Transit  Instrument  every  few  days.  In- 
deed, for  the  nicest  observations,  it  is  usual  not  to  at- 
tempt to  bring  the  clock  to  an  absolute  state  of  correct- 
ness, but  after  bringing  it  as  near  to  such  a  state  as  can 
conveniently  be  done,  to  ascertain  how  much  it  gains  or 
loses  in  a  day ;  that  is,  to  ascertain  its  rate  of  going,  and 
to  make  allowance  accordingly. 

94.  The  Transit  Instrument  is  adapted  to  taking  obser- 
vations on  the  meridian  only ;  but  we  sometimes  require 
to  know  the  altitude  of  a  celestial  body  when  it  is  not 
on  the  meridian,  and  its  azimuth,  or  distance  from  the 
meridian  measured  on  the  horizon.  An  instrument  es- 
pecially designed  to  measure  altitudes  and  azimuths,  is 
called  an  Altitude  and  Azimuth  Instrument,  whatever 
may  be  its  particular  form.  When  a  point  is  on  the  hor- 
izon its  distance  from  the  meridkm,  or  its  azimuth,  may 
be  taken  by  the  common  surveyor's  compass,  the  direc- 


94.  To  what  kind  of  observations  only  is  the  transit  instru- 
ment adapted  ?  What  instrument  is  employed  for  finding  alti- 
tude and  azimuth?  Describe  the  Altitude  and  Azimuth  In- 
stuiment  from  figure  13 


ASTRONOMICAL  INSTRUMENTS. 


61 


tion  of  the  meridian  being  determined  by  the  needle ; 
but  when  the  object,  as  a  star,  is  not  on  the  horizon,  its 
azimuth,  it  must  be  remembered,  is  the  arc  of  the  hori- 
zon from  the  meridian  to  a  vertical  circle  passing  through 
the  star ;  at  whatever  different  altitudes,  therefore,  two 
stars  may  be,  and  however  the  plane  which  passes 
through  them  may  be  inclined  to  the  horizon,  still  it  is 
their  angular  distance  measured  on  the  horizon  which 
determines  their  difference  of  azimuth.  Figure  13  rep- 
resents an  Altitude  and  Azimuth  Instrument,  several  of 
the  usual  appendages  and  subordinate  contrivances  being 
omitted  for  the  sake  of  distinctness  and  simplicity.  Here 
abc  is  the  vertical  or  altitude  circle,  and  EFG  the  hori- 
zontal or  azimuth  circle  ;  AB  is  a  telescope  mounted  on 

Fig.  13. 


a  horizontal  axis  and  capable  of  two  motions,  one  in  al- 
titude parallel  to  the  circle  abc,  and  the  other  in  azimuth 
parallel  to  EFG.  Hence  it  can  be  easily  brought  to 

6 


62  THE  EARTH. 

bear  upon  any  object.  At  m,  under  the  eye  glass  of  the 
telescope,  is  a  small  mirror  placed  at  an  angle  of  45° 
with  the  axis  of  the  telescope,  by  means  of  which  the 
image  of  the  object  is  reflected  upwards,  so  as  to  be 
conveniently  presented  to  the  eye  of  the  observer.  At  d 
is  represented  a  tangent  screw,  by  which  a  slow  motion 
is  given  to  the  telescope  at  c.  At  h  and  g  are  seen  two 
spirit  levels,  at  right  angles  to  each  other,  which  show 
when  the  azimuth  circle  is  truly  horizontal.  The  in- 
strument is  supported  on  a  tripod,  for  the  sake  of  greater 
steadiness,  each  foot  being  furnished  with  a  screw  for 
levelling. 

95.  The  SEXTANT  is  an  instrument  used  for  taking  the 
angular  distance  between  any  two  bodies  on  the  surface 
of  the  celestial  sphere,  by  reflecting  the  image  of  one  of 
the  bodies  so  as  to  coincide  with  the  other  body  as  seen 
directly.  It  is  particularly  valuable  for  measuring  celes- 
tial arcs  at  sea,  because  it  is  not,  like  most  astronomical 
instruments,  affected  by  the  motion  of  the  ship. 

This  instrument  (Fig  14,)  is  of  a  triangular  shape, 
and  is  made  strong  and  firm  by  metallic  crossbars.  It 
has  two  reflectors,  I  and  H,  called,  respectively,  the  Index 
Glass,  and  the  Horizon  Glass,  both  of  which  are  firmly 
fixed  perpendicular  to  the  plane  of  the  instrument.  The 
Index  Glass  is  attached  to  the  movable  arm  ID  and 
turns  as  this  is  moved  along  the  graduated  limb  EF. 
This  arm  also  carries  a  Vernier  at  D,  which  enables  us  to 
take  off  minute  parts  of  the  spaces  into  which  the  limb 
is  divided.  The  Horizon  Glass,  H,  consists  of  two 
parts  ;  the  upper  being  transparent  or  open,  so  that  the 
eye,  looking  through  the  telescope  T,  can  see  through 
it  a  distant  i>ody  as  a  star  at  S,  while  the  lower  part  is 
a  reflector. 


95.  Define  the  Sextant — For  what  is  it  particularly  valu- 
able ?  Describe  it  from  figure.  14.  Where  is  the  Vernier  and 
what  is  its  use  ?  Specify  the  manner  in  which  the  light  comes 
from  the  object  to  the  eye.  How  can  we  measure  the  angulai 
distance  between  the  moon  and  a  star  ? 


ASTRONOMICAL  INSTRUMENTS. 


63 


Suppose  it  were  required  to  measure  the  angular  dis- 
tance between  the  moon  and  a  certain  star,  the  moon 

Fig.  14. 


being  at  M ,  and  the  star  at  S.  The  instrument  is  held 
firmly  in  the  hand,  so  that  the  eye,  looking  through  the 
telescope,  sees  the  star  S  through  the  transparent  part  of 
the  Horizon  Glass.  Then  the  movable  arm  ID  is  moved 
from  F  towards  E,  until  the  image  of  M  is  carried  down 
to  S,  when  the  number  of  degrees  and  parts  of  a  degree 
reckoned  on  the x  limb  from  F  to  the  index  at  D,  will 
show  the  angular  distance  between  the  two  bodies. 


FIGURE  AND  DENSITY  OF  THE  EARTH. 

96.  We  have  already  shown,  that  the  figure  of  the 
earth  is  nearly  globular ;  but  since  the  semi-diameter  of 
the  earth  is  taken  as  the  base  line  in  determining  the 
parallax  of  the  heavenly  bodies,  and  lies  therefore  at  the 
foundation  of  all  astronomical  measurements,  it  is  very 


64  THE  EARTH. 

important  that  it  should  be  ascertained  with  the  greatest 
possible  exactness.  Having  now  learned  the  use  of  as- 
tronomical instruments,  and  the  method  of  measuring 
arcs  on  the  celestial  sphere,  we  are  prepared  to  under- 
stand the  methods  employed  to  determine  the  exact  fig- 
ure of  the  earth.  This  element  is  indeed  ascertained 
in  different  ways,  each  of  which  is  independent  of  all 
the  rest,  namely,  by  investigating  the  effects  of  the  cen- 
trifugal force  arising  from  the  revolution  of  the  earth 
on  its  axis — by  measuring  arcs  of  the  meridian — and  by 
experiments  with  the  pendulum. 

97.  First,  the  known  effects  of  the  centrifugal  force, 
would  give  to  the  earth  a  spheroidal  figure,  elevated  in 
the  equatorial,  and  flattened  in  the  polar  regions. 

By  the  centrifugal  force  is  meant,  the  tendency  which 
revolving  bodies  exhibit  to  recede  from  the 
Fig.  15.  center.  Thus  when  a  grindstone  is  turn- 
ed swiftly,  water  is  thrown  off  from  it  in 
.straight  lines.  The  same  effect  is  notic- 
ed when  a  carriage  wheel  is  driven  rapidly 
through  the  water.  If  a  pail,  containing 
a  little  water,  is  whirled,  the  water  rises 
on  the  sides  of  the  pail  in  consequence  of 
the  centrifugal  force.  The  same  principle 
is  more  strikingly  illustrated  by  the  annex- 
ed cut,  (Fig.  15,)  which  represents  an 
open  glass  vessel  suspended  by  a  cord  at- 
tached to  its  opposite  sides,  and  passed 
through  a  staple  in  the  ceiling  of  the  room. 
A  little  water  is  introduced  into  the  ves- 
sel which  is  made  to  whirl  rapidly  by  ap- 
plying the  hand  to  the  opposite  sides.  As 
it  turns,  the  water  rises  on  the  sides  of  the 
vessel,  receding  as  far  as  possible  from  the 


96.  Why  is  it  so  necessary  to  ascertain  accurately  the  semi- 
diameter  of  the  earth  ?  In  how  many  different  ways  is  this 
element  ascertained  ?  Specify  them.  What  is  meant  by  the 
centrifugal  force  ?  Give  an  illustration.  Describe  figure  15. 


ASTRONOMICAL  INSTRUMENTS.  65 

center.  The  same  effect  is  produced  by  suffering  the 
cord  to  untwist  freely,  which  gives  a  swift  revolution 
to  the  vessel.  In  like  manner,  a  ball  of  soft  clay  when 
made  to  turn  rapidly  on  its  axis,  swells  out  in  the  central 
parts  and  becomes  flattened  at  the  ends,  forming  the  fig- 
ure called  an  oblate  spheroid. 

Had  the  earth  been  originally  constituted  (as  geolo- 
gists suppose)  of  yielding  materials,  either  fluid  or  semi- 
fluid, so  that  its  particles  could  obey  their  mutual  at- 
traction, while  the  body  remained  at  rest  it  would  spon- 
taneously assume  the  figure  of  a  perfect  sphere  ;  as  soon, 
however,  as  it  began  to  revolve  on  its  axis,  the  greater 
velocity  of  the  equatorial  regions  would  give  to  them  a 
greater  centrifugal  force",  and  cause  the  body  to  swell 
out  into  the  form  of  an  oblate  spheroid.  Even  had  the 
solid  part  of  the  earth  consisted  of  unyielding  materials 
and  been  created  a  perfect  sphere,  still  the  waters  that 
covered  it  would  have  receded  from  the  polar  and  have 
been  accumulated  in  the  equatorial  regions,  leaving  bare 
extensive  regions  on  the  one  side,  and  ascending  to  a 
mountainous  elevation  on  the  other. 

On  estimating,  from  the  known  dimensions  of  the 
earth  and  the  velocity  of  its  rotation,  the  amount  of  the 
centrifugal  force  in  different  latitudes,  and  the  figure  of 
equilibrium  which  would  result,  Newton  inferred  that 
the  earth  must  have  the  form  of  an  oblate  spheroid  be- 
fore the  fact  had  been  established  by  observation  ;  and 
he  assigned  nearly  the  true  ratio  of  the  polar  and  equa- 
torial diameters. 


\  97.  What  would  be  the  figure  of  the  earth  derived  from  the 
centrifugal  force  ?  What  figure  would  the  earth  have  assumed 

:  if  at  rest  ?  How  would  this  figure  be  changed  when  it  began  to 
revolve  ?  Had  the  earth  been  originally  a  solid  sphere  covered 
with  water,  how  would  the  water  have  disposed  itself  when  the 
earth  was  made  to  turn  on  its  axis  ?  How  was  the  spheroidal 
figure  of  the  earth  inferred  before  the  fact  was  established  by 
observation  ? 

6* 


66 


THE  EARTH. 


98.  Secondly,  the.  spheroidal  figure  of  the  earth  is 
proved,  by  actually  measuring  the  length  of  a  degree  on 
the  meridian  in  different  latitudes. 

Were  the  earth  a  perfect  sphere,  the  section  of  it  made 
by  a  plane  passing  through  its  center  in  any  direction 
would  be  a  perfect  circle,  whose  curvature  would  be 
equal  in  all  parts ;  but  if  we  find  by  actual  observation, 
that  the  curvature  of  the  section  is  not  uniform,  we  in- 
fer a  corresponding  departure  in  the  earth  from  the  figure 
of  a  perfect  sphere.  The  task  of  measuring  portions  of 
the  meridian,  has  been  executed  in  different  countries. 
We  may  know,  in  each  case,  how  far  we  advance  on 
the  meridian,  because  every  step  we  take  northward, 
produces  a  corresponding  increase  in  the  altitude  of  the 
north  star.  That  an  increase  of  the  length  of  the  de- 
grees of  the  meridian,  as  we  advance  from  the  equator 
towards  the  pole,  really  proves  that  the  earth  is  flattened 
at  the  poles,  will  be  readily  seen  on  a  little  reflection. 
We  must  bear  in  mind  that  a  degree  is  not  any  certain 
length,  but  only  the  three  hundred  and  sixtieth  part  of  a 
circle,  whether  great  or  small.  If,  therefore,  a  degree  is 
longer  in  one  case  than  in  another,  we  infer  that  it  is  the 
three  hundred  and  sixtieth  part  of  a  larger  circle  ;  and 
since  we  find  that  a  degree  towards  the  pole  is  longer 
than  a  degree  towards  the  equator,  we  infer  that  the  cur- 
vature is  less  in  the  former  case  than  in  the  latter. 

The  result  of  all  the  measurements  is,  that  the  length 
of  a  degree  increases  as  we  proceed  from  the  equator 
towards  the  pole,  as  may  be  seen  from  the  following 
table : 


98.  By  what  measurements  is  the  spheroidal  figure  of  the 
earth  proved  ?  What  would  be  the  curvature  in  all  parts  were 
the  earth  a  perfect  sphere  ?  How  may  we  know  when  we  have 
advanced  one  degree  northward  in  the  meridian  ?  Explain  how 
an  increase  of  the  length  of  a  degree  proves  that  the  earth  is 
flattened  towards  the  poles  ?  In  what  places  hive  arcs  of  the  me- 
ridian been  measured  7  What  is  the  mean  diameter  of  the 
earth  ?  What  is 'the  difference  between  the  two  diameters  ? 
What  fraction  expresses  the  ellipticity  of  the  earth  ? 


ASTRONOMICAL  INSTRUMENTS. 


67 


Places  of  observation. 

Latitude. 

Length  of  a  degree  in  miles 

Peru, 
Pennsylvania, 
Italy, 
France, 
England, 
Sweden, 

00°  00'  00" 
30    12  00 
43    01   00 
46    12  00 
51    29  541 
66    20   10 

68.732 
68.896 
68.998 
69.054 
69.164 
69.292 

Combining  the  results  of  various  estimates,  the  di- 
mensions of  the  terrestrial  spheroid  are  found  to  be  as 
follows : 

Equatorial  diameter,  .  .  .  7925.648 
Polar  diameter,  ....  7899.170 
Mean  diameter,  ,  7912.409 

The  difference  between  the  greatest  and  the  least,  is 
26.478  =  ^9  of  the  greatest.  This  fraction  (^Q)  is  de- 
nominated the  ellipticity  of  the  earth,  being  the  excess 
of  the  longest  over  the  shortest  diameter. 

99.  Thirdly,  the  figure  of  the  earth  is  shown  to  be 
spheroidal,  by  observations  with  the  pendulum. 

If  a  pendulum,  like  that  of  a  clock,  be  "suspended 
and  the  number  of  its  vibrations  per  hour  be  counted, 
they  will  be  found  to  be  different  in  different  latitudes. 
A  pendulum  that  vibrates  3600  times  per  hour  at  the 
equator,  will  vibrate  3605J  times  at  London,  and  a  still 
greater  number  of  times  nearer  the  north  pole.  Now  the 
vibrations  of  the  pendulum  are  produced  by  the  force  of 


96.  Explain  how  we  may  ascertain  the  figure  of  the  earth  by 
means  of  a  pendulum — How  will  the  number  of  vibrations  be 
in  different  latitudes  ?  How  many  times  will  a  pendulum  vi- 
brate in  an  hour  at  London,  which  vibrates  3600  times  per  hour 
at  the  equator  ?  How  are  the  vibrations  of  the  pendulum  pro- 
duced ?  Why  are  these  comparative  numbers  at  different 
places  measures  of  the  relative  distances  from  the  center  of  the 
earth  ?  What  could  we  infer  from  two  observations  with  the 
pendulum,  one  at  the  equator  and  the  other  at  the  north  pole  ? 
To  what  conclusions  have  pendulum  observations,  made  in  va- 
rious parts  of  .he  earth,  led  ? 


THE  EARTH. 


gravity.  Hence  their  comparative  number  at  different 
places  is  a  measure  of  the  relative  forces  of  gravity  at 
those  places.  But  when  we  know  the  relative  forces  of 
gravity  at  different  places,  we  know  their  relative  dis- 
tances from  the  center  of  the  earth,  because  the  nearer  a 
place  is  to  the  center  of  the  earth,  the  greater  is  the  force 
of  gravity.  Suppose,  for  example,  we  should  count  the 
number  of  vibrations  of  a  pendulum  at  the  equator,  and 
then  carry  it  to  the  north  pole  and  count  the  number  of 
.vibrations  made  there  in  the  same  time  ;  we  should  be 
able  from  these  two  observations  to  estimate  the  relative 
forces  of  gravity  at  these  two  points  ;  and  having  the  rel- 
ative forces  of  gravity,  we  can  thence  deduce  their  rela- 
tive distances  from  the  center  of  the  earth,  and  thus  ob- 
tain the  polar  and  equatorial  diameters.  Observations 
of  this  kind  have  been  taken  with  the  greatest  accuracy 
in  many  places  on  the  surface  of  the  earth,  at  various 
distances  from  each  other,  and  they  lead  to  the  same 
conclusions  respecting  the  figure  of  the  earth,  as  those 
derived  from  measuring  arcs  of  the  meridian. 

100.  The  density  of  the  earth  compared  with  water, 
that  is,  its  specific  gravity,  is  5^0  The  density  was  first 
estimated  by  Dr.  Hutton,  from  observations  made  by  Dr. 
Maskelyne,  Astronomer  Royal,  on  Schehallien,  a  moun- 
tain of  Scotland,  in  the  year  1774.  Thus,  let  M  (Fig. 
16,)  represent  the  mountain,  D,  B,  two  stations  on  op- 
posite sides  of  the  mountain,  and  I  a  star ;  and  let  IE 
and  IG  be  the  zenith  distances  as  determined  by  the 
difference  of  latitude  of  the  two  stations.  But  the  ap- 
parent zenith  distances  as  determined  by  the  plumb  line 
are  IE'  and  IG'.  The  deviation  towards  the  mountain 
on  each  side  exceeded  7".  The  attraction  of  the  moun- 
tain being  observed  on  both  sides  of  it,  and  its  mass  be- 
ing computed  from  a  number  of  sections  taken  in  all  di 


100  What  is  the  specific  gravity  of  the  earth  ?  How  was  it 
ascertained?  "Explain  figure  16.  Why  is  the  density  of  the 
earth  so  important  an  element  ? 


DENSITY  OF  THE  EARTH. 


69 


rections,  tnese  data,  when  compared  with  the  known 
attraction  and  magnitude  of  the  earth,  led  to  a  knowl- 
edge of  its  mean  density.  According  to  Dr.  Hutton, 
this  is  to  that  of  water  as  9  to  2  ;  but  later  and  more  ac- 
curate estimates  have  made  the  specific  gravity  of  the 
earth  as  stated  above.  But  this  density  is  nearly  double 
the  average  density  of  the  materials  that  compose  the 
exterior  crust  of  the  earth,  showing  a  great  increase  of 
density  towards  the  center. 

The  density  of  the  earth  is  an  important  element,  as 
we  shall  find  that  it  helps  us  to  a  knowledge  of  the  den- 
sity of  each  of  the  other  members  of  the  solar  system. 


OF 


PART  II. OF  THE  SOLAR  SYSTEM. 


101.  HAVING  considered  the  Earth,  in  its  astronomical 
relations,  and  the  Doctrine  of  the  Sphere,  we  proceed 
now  to  a  survey  of  the  Solar  System,  and  shall  treat  suc- 
cessively of  the  Sun,  Moon,  Planets,  and  Comets. 


CHAPTER     I. 

OF  THE  SUN SOLAR  SPOTS ZODIACAL  LIGHT. 

102.  THE  figure  which  the  sun  presents  to  us  is  that 
\f  a  perfect  circle,  whereas  most  of  the  planets  exhibit  a 
jisk  more  or  less  elliptical,  indicating  that  the  true  shape 
of  the  body  is  an  oblate  spheroid.     So  great,  however, 
is  the  distance  of  the  sun,  that  a  line  400  miles  long 
would  subtend  an  angle  of  only  I"  at  the  eye,  and  would 
therefore  be  the  least  space  that  could  be  measured. 
Hence,  were  the  difference  between  two  conjugate  di- 
ameters of  the  sun  any  quantity  less  than  this,  we  could 
not  determine  by  actual  measurement  that  it  existed  at 
all.       Still  we  learn  from   theoretical   considerations, 
founded  upon  the  known  effects  of  centrifugal  force, 
arising  'from  the   sun's  revolution  on  his  axis,  that  his 
figure  is  not  a  perfect  sphere,  but  is  slightly  spheroidal. 

103.  The  distance  of  the  sun  from  the  earth,  is  nearly 
95,000,000  miles.     In  order  to  form  some  faint  concep- 


101.  What  subjects  are  treated  of  in  Part  II 

102.  What  figure  does  the  sun  present  to  us  ?     What  angle 
would  a  line  of  400  miles  on  the  sun's  disk  subtend  ?     How  is 
it  inferred  that  the  figure  of  the  sun  is  spheroidal  1 


DENSITY.  71 

tion  at  least  of  this  vast  distance,  let  us  reflect  that  a  rail- 
way car,  moving  at  the  rate  of  20  miles  per  hour,  would 
require  more  than  500  years  to  reach  the  sun. 

The  apparent  diameter  of  the  sun  is  a  little  more  than 
half  a  degree,  (32'  3X/.)  Its  linear  diameter  is  about 
885,000  miles ;  and  since  the  diameter  of  the  earth  is 
only  7912  miles,  the  latter  number  is  contained  in  the 
former  nearly  112  times ;  so  that  it  would  require  one 
hundred  and  twelve  bodies  like  the  earth,  if  laid  side  by 
side,  to  reach  across  the  diameter  of  the  sun  ;  and  a  ship 
sailing  at  the  rate  of  ten  miles  an  hour,  would  require 
more  than  ten  years  to  sail  across  the  solar  disk. 

The  sun  is  about  1,400,000  times  as  large  as  the  earth. 
The  distance  of  the  moon  from  the  earth  being  238,000 
miles,  were  the  center  of  the  sun  made  to  coincide  with 
the  center  of  the  earth,  the  sun  would  extend  every  way 
from  the  earth  nearly  twice  as  far  as  the  moon. 

104.  In  density,  the  sun  is  only  one-fourth  that  of  the 
earth,  being  but  a  little  heavier  than  water-;  and  the 
quantity  of  matter  in  the  sun  is  three  hundred  and  fifty 
thousand  times  as  great  as  in  the  earth.  A  body  would 
weigh  nearly  28  times  as  much  at  the  sun  as  at  the 
earth.  A  man  weighing  200  Ibs.  would,  if  transported 
to  the  surface  of  the  sun,  weigh  5,580  Ibs.,  or  nearly  2 \ 
tons.  To  lift  one's  limb,  would,  in  such  a  case,  be  be- 
yond the  ordinary  power  of  the  muscles.  At  the  surface 
of  the  earth,  a  body  falls  through  16r^feet  in  a  second  • 

103.  What  is  the  distance  of  the  sun  from  the  earth  ?    How 
long  would  a  railway  car,  moving  at  the  rate  of  20  miles  per 
hour,  require  to  reach  the  sun  ?     How  many  bodies  equal  to 
the  earth  could  lie  side  by  side   across  tho  sun  ?     How  long 
would  a  ship  be  in  sailing  across  it  at  10  miles  an  hour  ?     If 
the  sun's  center  were  made  to  coincide  with  the  center  of  the 
earth,  how  much  farther  would  it  reach  than  the  moon  ?   What  • 
is  the  sun's  apparent  diameter  ?     What  is  its  linear  diameter  ? 

104.  In  density  how  does  the  sun  compare  with  the  earth? 
How  in  quantity  of  matter  ?     How  much  more  would  a  body 
weigh  at  the  sun  than  at  the  earth  ?     How  far  would  a  body 
fall  in  one  second  at  the  surface  of  the  sun  ? 


72  THE  SUN. 

but  a  body  would  fall  at  the  sun  in  one  second  through 
448.7  feet. 

SOLAR  SPOTS. 

105.  The  surface  of  the  sun,  when  viewed  with  a 
telescope,  usually  exhibits  dark  spots,  which  vary  much, 
at  different  tinmss,  in  number,  figure,  and  extent.  One 
hundred  or  more,  assembled  in  several  distinct  groups, 
are  sometimes  visible  at  once  on  the  solar  disk.  Tl?e 
greatest  part  of  the  solar  spots  are  commonly  very  small, 
but  occasionally  a  spot  of  enormous  size  is  seen  occupy- 
ing an  extent  of  50,000  miles  in  diameter.  They  are 
sometimes  even  visible  to  the  naked  eye.  when  the  sun 
is  viewed  through  colored  glass,  or,  when  near  the  hori- 
zon, it  is  seen  through  light  clouds  or  vapours.  When  it 
is  recollected  that  I"  of  the  solar  disk  implies  an  extent 
of  400  miles,  it  is  evident  that  a  space  large  enough  to  be 
seen  by  the  naked  eye,  must  cover  a  very  large  extent. 

A  solar  spot  usually  consists  of  two  parts,  the  nucleus 
and  the  umbra,  (Fig.  17.)  The  nucleus  is  black,  of  a 

rig.  n: 


105.  Solar  spots. — Are  they  constant  or  variable  in  number 
and  appearance  ?  How  many  are  sometimes  seen  on  the  sun's 
disk  at  once  1  Are  they  usually  large  or  small  ?  How  many 
miles  in  diameter  are  the  largest  ?  Describe  a  spot.  What 
changes  occur  in  the  nucleus  ?  What  is  the  umbra  ?  In  what 
part  of  the  sun  do  the  spots  mostly  appear  ?  What  apparent 
motions  have  they  ?  What  is  the  period  of  their  revolution  ? 


SOLAR  SPOTS. 


73 


very  irregular  shape,  and  is  subject  to  great  and  sudden 
changes,  both  in  form  and  size.  Spots  have  sometimes 
seemed  to  burst  asunder,  and  to  project  fragments  in  dif- 
ferent directions.  The  umbra  is  a  wide  margin  of 
lighter  shade,  and  is  often  of  greater  extent  than  the 
nucleus.  The  spots  are  usually  confined  to  a  zone  ex- 
tending across  the  central  regions  of  the  sun,  not  exceed- 
ing 60°  in  breadth.  When  the  spots  are  observed  from 
day  to  day,  they  are  seen  to  move  across  the  disk  of  the 
sun,  occupying  about  two  weeks  in  passing  from  one 
limb  to  the  other.  After  an  absence  of  about  the  same 
period,  the  spot  returns,  having  taken  27d.  7h.  37m.  in 
the  entire  revolution. 


106.  The  spots  must  be  nearly 
or  quite  in  contact  with  the  body 
of  the  sun.  Were  they  at  any 
considerable  distance  from  it,  the 
time  during  which  they  would 
be  seen  on  the  solar  disk,  would 
be  less  than  that  occupied  in 
the  remainder  of  the  revolution. 
Thus,  let  S,  (Fig.  18,)  be  the 
sun,  E  the  earth,  and  abc  the  path 
of  the  body,  revolving  about 
the  sun.  Unless  the  spot  were 
nearly  or  quite  in  contact  with 
the  body  of  the  sun,  being  pro- 
jected upon  his  disk  only  while 
passing  from  b  to  c,  and  being 
invisible  while  describing  the 
arc  cab,  it  would  of  course  be 
out  of  sight  longer  than  in  sight, 
whereas  the  two  periods  are 
found  to  be  equal.  Moreover, 


Fig.  18 


106.  How  are  the  spots  known  to  be  nearly  or  quite  in  con- 
tact with  the  body  of  the  sun  ?  Illustrate  by  figure  18.  What 
causes  the  motion  of  the  spots  ?  What  is  the  period  of  the  sun's 
revolution  on  his  axis  *  Explain  by  figure  19. 

7 


74 


THE  SUN. 


the  lines  which  all  the  solar  spots  describe  on  the  disk 
of  the  sun,  are  found  to  be  parallel  to  each  other,  like 
the  circles  of  diurnal  revolution  around  the  earth,  and 
hence  it  is  inferred  that  they  arise  from  a  similar  cause, 
namely,  the  revolution  of  the  sun  on  its  axis,  a  fact  which 
is  thus  made  known  to  us. 

But  although  the  spots  occupy  about  27-J-  days  in  pass- 
ing from  one  limb  of  the  sun  around  to  the  same  limb 
again,  yet  this  is  not  the  period  of  the  sun's  revolution 
on  his  axis,  but  exceeds  it  by  nearly  two  days.  For, 
let  AA'B  (Fig.  19,)  represent  the  sun,  and  EE'M  the 
orbit  of  the  earth.  Thus,  when  the  earth  is  at  E,  the 
visible  disk  of  the  sun  will  be 
AA'B ;  and  if  the  earth  remain- 
ed stationary  at  E,  the  time  oc- 
cupied by  a  spot  after  leaving  A 
until  it  returned  to  A,  would  be 
just  equal  -to  the  time  of  the 
sun's  revolution  on  his  axis. 
But  during  the  27J  days  in 
which  the  spot  has  been  per- 
forming its  apparent  revolution, 
the  earth  has  been  advancing 
in  his  orbit  from  E  to  E',  where 
the  visible  disk  of  the  sun  is 

A'B'.  Consequently,  before  the  spot  can  appear  again 
on  the  limb  from  which  it  set  out,  it  must  describe  so 
much  more  than  an  entire  revolution  as  equals  the  arc 
AAX,  and  this  occupies  nearly  two  days,  which  sub- 
tracted from  27^  days,  makes  the  sun's  revolution  on 
its  axis  about  25J  days  ;  or  more  accurately,  it  is  25d. 
9h.  56m. 

107.  A  telescope  of  moderate  powers  is  sufficient  to 
show  the  spots  on  the  sun,  and  it  is  earnestly  recom- 
mended to  the  learner  to  avail  himself  of  the  first  oppor- 


107.  How  large  a  telescope  is  sufficient  to  view  the  spots  on 
the  sun  ?  How  is  the  eye  protected  from  the  glare  of  the  sun's 
light  ?  How  may  these  shades  be  made  ? 


SOLAR  SPOTS.  75 

tunity  he  may  have,  to  view  them  for  himself.  For  ob- 
servations on  the  sun,  telescopes  are  usually  furnished 
with  colored  glass  shades,  which  are  screwed  upon  the 
end  of  the  instrument  to  which  the  eye  is  applied,  foi 
the  purpose  of  protecting  the  eye  from  the  glare  of  the 
sun's  light.  Such  screens  may  be  easily  made  by  hold- 
ing a  small  piece  of  window  glass  over  the  flame  of  a 
lamp,  the  wick  being  raised  higher  than  usual  so  as  to 
smoke  freely. 

108.  The  cause  of  the  solar  spots  is  unknown.  It  is 
not  easy  to  determine  what  it  is  that  occasions  such 
changes  on  the  surface  of  the  sun ;  but  various  conjec- 
tures have  been  proposed  by  different  astronomers.  Ga- 
lileo supposed  that  the  dark  part  of  a  spot  is  owing  to 
black  cinders  which  rise  from  the  interior  of  the  sun, 
where  they  are  formed  by  the  action  of  heat,  constitu- 
ting a  kind  of  volcanic  lava  that  floats  upon  the  surface 
of  the  fiery  flood,  which  he  supposed  to  constitute  the 
outer  portion  of  the  sun.  But  the  vast  extent  which 
these  spots  occasionally  assume  is  unfavourable  to  such  a 
supposition.  It  is  incredible  that  a  quantity  of  volcanic 
lava  should  suddenly  rise  to  the  surface  of  the  sun,  suffi- 
cient to  occupy  (as  a  spot  is  sometimes  found  to  do) 
2000,000,000  s'quare  miles. 

Dr.  Herschel  proposed  a  theory  respecting  the  nature 
*  nd  constitution  of  the  sun,  which,  more  from  respect 
;,o  his  authority  than  on  account  of  any  evidence  by 
which  it  is  supported,  has  been  generally  received.  Ac- 
cording to  him,  the  sun  is  itself  an  opake  body  like  the 
earth,  but  is  envelpped  at  a  considerable  distance  from 
his  body  by  two  different  strata  of  clouds,  the  exterior 


108.  Is  the  cause  of  solar  spots  well  known  ?  What  was 
Galileo's  hypothesis  ?  What  objections  are  there  against  it  1 
What  is  Herschel's  theory  of  the  nature  and  constitution  of 
ihe  sun  ?  What  sort  of  a  body  does  he  consider  the  sun  itself? 
By  what  is  it  encompassed  ?  Where  is  the  repository  of  the 
sun's  light  and  heat  ?  How  does  he  explain  the  spots  ?  What 
objections  are  there  to  this  theory  ?  What  are  faculeB  ? 


76  THE  SUN. 

stratum  being  the  fountain  from  which  emanates  the 
sun's  light  and  heat.     The  solar  spots  arise  from  the  oc- 
casional displacement  of  portions  of  this  envelope  of 
clouds,  disclosing  to  view  tracts  of  the  solid  body  of  tl 
sun. 

We  regard  this  view  of  the  origin  of  the  sun's  light  ar, 
heat  as  unsubstantiated  by  any  satisfactory  proofs,  ar 
as  in  itself  highly  improbable.  Such  a  medium  wou] 
be  a  very  unsuitable  repository  for  the  intense  heat  < 
the  sun,  which  can  arise  only  from  fixed  matter  in  a  stai 
of  high  ignition.  The  most  probable  supposition  is,  thi 
the  surface  of  the  sun  consists  of  melted  matter  in  sue 
a  state.  We  must  confess  our  ignorance  of  any  know 
cause  which  is  adequate  to  explain  the  sudden  extinc- 
tion and  removal  of  so  large  portions  of  this  fiery  flood, 
as  is  occupied  by  some  of  the  solar  spots. 

Besides  the  dark  spots  on  the  sun,  there  are  also  seen, 
in  different  parts,  places  that  are  brighter  than  the  neigh- 
boring portions  of  the  disk.  These  are  called  faculce. 
Other  inequalities  are  observable  in  powerful  telescopes, 
all  indicating  that  the  surface  of  the  sun  is  in  a  state  of 
constant  and  powerful  agitation. 

ZODIACAL  LIGHT. 

109.  The  Zodiacal  Light  is  a  faint  light  resembling 
the  tail  of  a  comet,  and  is  seen  at  certain  seasons  of  the 
year  following  the  course  of  the  sun  after  evening  twi- 
light, or  preceding  his  approach  in  the  morning  sky. 
Figure  20  represents  its  appearance  as  seen  in  the  even- 
ing in  March,  1836.  The  following  are  the  leading  facts 
respecting  it. 

1.  Its  form  is  that  of  a  luminpus  pyramid,  having  its 
base  towards  the  sun.  It  reaches  to  an  immense  dis- 
tance from  the  sun,  sometimes  even  beyond  the  orbit  of 
the  earth.  It  is  brighter  in  the  parts  nearer  the  sun  than 
in  those  that  are  more  remote,  and  terminates  in  an  ob- 
tuse apex,  its  light  fading  away  by  insensible  gradations, 
until  it  becomes  too  feeble  for  distinct  vision.  Hence 
its  limits  are  at  the  same  time  fixed  at  different  dis- 


ZODIACAL    LIGHT.  77      , 

Fig.  2,). 


lances  from  the  sun  by  different  observers,  according  to 
their  respective  powers  of  vision. 

2.  Its  aspects  vary  very  much  with  the  different  seasons 
of  the  year.  About  the  first  of  October,  in  our  climate 
(Lat.  41°  18')  it  becomes  visible  before  the  dawn  of  day. 
rising  along  north  of  the  ecliptic,  and  terminating  above 
the  nebula  of  Cancer.  About  the  middle  of  November, 
its  vertex  is  in  the  constellation  Leo.  At  this  time  no 
traces  of  it  are  seen  in  the  west  after  sunset,  but  about 
the  first  of  December  it  becomes  faintly  visible  in  the 
west,  crossing  the  Milky  Way  near  the  horizon,  and 
reaching  from  the  sun  to  the  head  of  Capricornus,  form- 
ing, as  its  brightness  increases,  a  counterpart  to  the  Milky 


109.  Zodiacal  Light. — -Describe  it.  When  and  where 
seen  ?  What  is  its  form  1  How  far  does  it  reach  ?  Where 
brightest  ?  How  do  its  aspects  vary  at  different  seasons  of 
the  year  ?  What,  motions  has  it  ?  Is  it  equally  conspicuous 
every  year  ?  What  was  it  formerly  held  to  be  ?  With  what 
phenomenon  has  it  been  supposed  to  be  connected  ? 

7* 


78  THE    SUN. 

Way,  between  which  on  the  right,  and  the  Zodiacal 
Light  on  the  left,  lies  a  triangular  space  embracing  the 
Dolphin.  Through  the  month  of  December,  the  Zo- 
diacal Light  is  seen  on  both  sides  of  the  sun,  namely, 
before  the  morning  and  after  the  evening  twilight,  some- 
times extending  50°  westward,  and  70°  eastward  of  the 
sun  at  the  same  time.  After  it  begins  to  appear  in  the 
western  sky,  it  increases  rapidly  from  night  to  night, 
both  in  length  and  brightness,  and  withdraws  itself  from 
the  morning  sky,  where  it  is  scarcely  seen  after  the 
month  of  December,  until  the  next  October. 

3.  The  Zodiacal  Light  moves  through  the  heavens  in 
the  order  of  the  signs.     It  moves  with  unequal  velocity, 
being  sometimes  stationary  and  sometimes  retrogade, 
while  at  other  times  it  advances  much  faster  than  the 
sun.     In  February  and  March,  it  is  very  conspicuous  in 
the  west,  reaching  to  the  Pleiades  and  beyond  ;  but  in 
April  it  becomes  more  faint,  and  nearly  or  quite  disap- 
pears during  the  month  of  May.     It  is  scarcely  seen  in 
this  latitude  during  the  summer  months. 

4.  It  is  remarkably  conspicuous  at  certain  periods  of 
a  few  years,  and  then  for  a  long  interval  almost  disap- 
pears. 

5.  The  Zodiacal  Light  was  formerly  held  to  be  the 
atmosphere  of  the  sun.     But  La  Place  has  shown  that 
the  solar  atmosphere  could  never  reach  so  far  from  the 
sun  as  this  light  is  seen  to  extend.     It  has  been  supposed 
by  others  to  be  a  nebulous  body  revolving  around  the 
sun.     The  author  of  this  work  has  ventured  to  suggest 
the  idea,  that  the  extraordinary  Meteoric  Showers,  which 
at  different  periods  visit  the  earth,  especially  in  the 
month  of  November,  may  be  derived  from  this  body. 
See  American  Journal  of  Science,  Vol.  29,  p.  378. 


79 


CHAPTER   II 

OF  THE  APPARENT  ANNUAL    MOTION  OF  THE  SUN — SEASONS 
FIGURE  OF  THE  EARTH'S  ORBIT. 

110.  THE  revolution  of  the  earth  around  the  sun  once 
a  year,  produces  an  apparent  motion  of  the  sun  around 
the  earth  in  the  same  period.  When  bodies  are  at  such 
a  distance  from  each  other  as  the  earth  and  the  sun,  a 
spectator  on  either  would  project  the  other  body  upon 
the  concave  sphere  of  the  heavens,  always  seeing  it  on 
the  opposite  side  of  a  great  circle,  180°  from  himself. 
Thus  when  the  earth  arrives  at  Libra  (Fig.  21,)  we  see 

Fig.  21. 


the  sun  in  the  opposite  sign  Aries.  When  the  earth 
moves  from  Libra  to  Scorpio,  as  we  are  unconscious  of 
our  own  motion,  the  sun  it  is  that  appears  to  move  from 
Aries  to  Taurus,  being  always  seen  in  the  heavens,  where 


80  THE  SUN. 

a  line  drawn  from  the  eye  of  the  spectator  through  the 
body  meets  the  concave  sphere  of  the  heavens.  Hence 
the  line  of  projection  carries  the  sun  forward  on  one 
side  of  the  ecliptic,  at  the  same  rate  as  the  earth  moves 
on  the  opposite  side  ;  and  therefore,  although  we  are  un- 
conscious of  our  own  motion,  we  can  read  it  from  day  to 
day  in  the  motions  of  the  sun.  If  we  could  see  the  stars 
at  the  same  time  with  the  sun,  we  could  actually  observe 
from  day  to  day  the  sun's  progress  through  them,  as  we 
observe  the  progress  of  the  moon  at  night ;  only  the 
sun's  rate  of  motion  would  be  nearly  fourteen  times 
slower  than  that  of  the  moon.  Although  we  do  not  see 
the  .stars  when  the  sun  is  present,  yet  after  the  sun  is  set, 
we  can  observe  that  it  makes  daily  progress  eastward, 
as  is  apparent  from  the  constellations  of  the  Zodiac  oc- 
cupying, successively,  the  western  sky  after  sunset,  pro- 
ving that  either  all  the  stars  have  a  common  motion  east- 
ward independent  of  their  diurnal  motion,  or  that  the 
sun  has  a  motion  -past  them,  from  west  to  east.  We' 
shall  see  hereafter  abundant  evidence  to  prove,  that  this 
change  in  the  relative  position  of  the  sun  and  stars,  is 
owing  to  a  change  in  the  apparent  place  of  the  sun, 
and  not  to  any  change  in  the  stars. 

111.  Although  the  apparent  revolution  of  the  sun  is 
in  a  direction  opposite  to  the  real  motion  of  the  earth,  as 
regards  absolute  space,  yet  both  are  nevertheless  from 
west  to  east,  since  these  terms  do  not  refer  to  any  direc- 
tions in  absolute  space,  but  to  the  order  in  which  certain 
constellations  (the  constellations  of  the  Zodiac)  succeed 
one  another.  The  earth  itself,  on  opposite  sides  of  its 
orbit,  does  in  fact  move  towards  directly  opposite  points 


110.  What  produces  the  apparent  motion  of  the  sun  around 
the  earth  once  a  year  ?  How  would  a  spectator  on  either  body 
see  the  other  ?  When  the  earth  is  at  Libra,  where  does  the 
sun  appear  to  be  ?  Explain  figure  21.  If  the  stars  were  visi- 
ble in  the  day  time,  how  could  we  determine  the  sun's  path  ? 
What  change  do  the  constellations  of  the  Zodiac  undergo  with 
respect  to  the  sun  ? 


ANNUAL  MOTION.  81 

of  space ;  but  it  is  all  the  while  pursuing  its  course  in 
the  order  of  the  signs.  In  the  same  manner,  although 
the  earth  turns  on  its  axis  from  west  to  east,  yet  any 
place  on  the  surface  of  the  earth  is  moving  in  a  direc- 
tion in  space  exactly  opposite  to  its  direction  twelve 
hours  before.  If  the  sun  left  a  visible  trace  on  the  face 
of  the  sky,  the  ecliptic  would  of  course  be  distinctly 
marked  on  the  celestial  sphere  as  it  is  on  an  artificial 
globe  ;  and  were  the  equator  delineated  in  a  similar  man- 
ner, (by  any  method  like  that  supposed  in  Art.  33,)  we 
should  'then  see  at  a  glance  the  relative  position  of  these 
two  circles,  the  points  where  they  intersect  one  another 
constituting  the  equinoxes,  the  points  where  they  are  at 
the  greatest  distance  asunder,  or  the  solstices,  and  vari- 
ous other  particulars,  which  for  want  of  such  visible 
traces,  we  are  now  obliged  to  search  for  by  indirect  and 
circuitous  methods.  It  will  even  aid  the  learner  to  have 
constantly  before  his  mental  vision,  an  imaginary  delin- 
eation of  these  two  important  circles  on  the  face  of  the 
sky. 

112.  The  equator  makes  an  angle  with  the  ecliptic  oj 
23°  28'.  This  is  called  the  obliquity  of  the  ecliptic. 
As  the  sun  and  earth  are  both  always  in  the  ecliptic,  and 
as  the  motion  of  the  earth  in  one  part  of  it  makes  the 
sun  appear  to  move  in  the  opposite  part  at  the  same  rate, 
the  sun  apparently  descends  in  the  winter  23°  28'  to  the 
south  of  the  equator,  and  ascends  in  the  summer  the 
same  number  of  degrees  to  the  north  of  it.  We  must 
keep  in  mind  that  the  celestial  equator  and  the  celestial 
ecliptic  are  here  understood,  and  we  may  imagine  them 


111.  In  what  sense  are  the  motions  of  the  sun  and  earth 
opposite,  and  in  what  sense  in  the  same  direction  ?     If  the 
ecliptic  and  equator  were  distinctly  delineated  on  the  face  of 
the  sky,  what  points  in  them  could  be  easily  observed  ? 

112.  What  angle  does  the  equator  make  with  the  ecliptic? 
In  what  circle  do  the  sun  and  earth  always  appear  ?     How  far 
do  they  recede  from  the  equator  ?     How  does  the  obliquity  oi 
the  ecliptic  vary  ? 


82  THE  SUN. 

to  be  two  great  circles  distinctly  delineated  on  the  face 
of  the  sky.  On  comparing  observations  made  at  differ- 
ent periods  for  more  than  two  thousand  years,  it  is  found, 
that  the  obliquity  of  the  ecliptic  is  not  constant,  but 
that  it  undergoes  a  slight  diminution  from  age  to  age, 
amounting  to  52"  in  a  century,  or  about  half  a  second 
annually.  We  might  apprehend  that  by  successive  ap- 
proaches to  each  other  the  equator  and  ecliptic  would 
finally  coincide  ;  but  astronomers  have  found  by  a  most 
profound  investigation,  founded  on  the  principles  of 
universal  gravitation,  that  this  variation  is  confined  with- 
in certain  narrow  limits,  and  that  the  obliquity,  after  di- 
minishing for  some  thousands  of  years,  will  then  in- 
crease for  a  similar  period,  and  will  thus  vibrate  for  ever 
about  a  mean  value. 

113.  Let  us  conceive  of  the  sun  as  at  that  point  of  the 
ecliptic  where  it  crosses  the  equator,  that  is,  at  one  of  the 
equinoxes,  as  the  vernal  equinox.  Suppose  he  stands 
still  then  for  twenty  four  hours.  The  revolution  of  the 
earth  on  its  axis  from  east  to  west  during  this  twenty 
four  hours,  will  make  the  sun  appear  to  describe  a  great 
circle  from  east  to  west,  coinciding  with  the  equaton 
At  the  end  of  this  period,  suppose  the  sun  to  move 
northward  one  degree  and  to  remain  there  for  the  next 
twenty-four  hours,  in  which  time  the  revolution  of  the 
earth  will  make  the  sun  appear  to  describe  another  cir- 
cle from  east  to  west,  parallel  to  the  equator,  but  one 
degree  north  of  it.  Thus  we  may  conceive  of  the  sun 
as  moving  one  degree  every  day  for  about  three  months, 
when  it  will  reach  the  point  of  the  ecliptic  farthest 
from  the  equator,  which  is  called  the  tropic  from  a  Greek 


113.  Suppose  the  sun  to  start  from  the  equator  and  to  ad- 
vance one  degree  north  daily,  explain  its  apparent  diurnal  rev- 
olutions. When  is  the  sun  at  the  northern  tropic  ?  When  is 
he  at  the  southern  tropic  ?  How  are  the  respective  meridian 
altitudes  of  the  sun  at  these  periods  ?  How  do  we  find  from 
*hese  observations,  the  obliquity  of  the  ecliptic  ? 


THE  SEASONS.  83 

word  (i^errw)  which  signifies  to  turn,  because  when  the 
sun  arrives  at  this  point,  his  motion  in  his  orbit  carries 
him  continually  towards  the  equator,  and  therefore  he 
seems  to  turn  about. 

When  the  sun  is  at  the  northern  tropic,  which  hap- 
pens about  the  21st  of  June,  his  elevation  above  the 
southern  horizon  at  noon,  is  the  greatest  of  the  year ; 
and  when  he  is  at  the  southern  tropic,  about  the  21st 
of  December,  his  elevation  at  noon  is  the  least  in  the 
year.  The  difference  between  these  two  meridian  alti- 
tudes, will  give  the  whole  distance  from  one  tropic  to 
the  other,  and  consequently  twice  the  distance  from  each 
tropic  to  the  equator.  By  this  means  we  find  how  far 
the  tropic  is  from  the  equator,  and  that  gives  us  the  in- 
clination of  the  two  circles  to  one  another  ;  for  the  great- 
est distance  between  any  two  great  circles  on  the  sphere, 
is  always  equal  to  the  angle  which  they  make  with  each 
other. 

114.  The  dimensions  of  the  earth's  orbit,  when  com- 
pared with  its  own  magnitude,  are  immense. 

Since  the  distance  of  the  earth  from  the  sun  is 
95,000,000  miles,  and  the  length  of  the  entire  orbit  nearly 
000,000,000  miles,  it  will  be  found,  on  calculation,  that 
the  earth  moves  1,640,000  miles  per  day,  68,000  miles 
per  hour,  1,100  miles  per  minute,  and  nearly  19  miles 
every  second,  a  velocity  nearly  sixty  times  as  great  as 
the  maximum  velocity  of  a  cannon  ball.  A  place  on 
the  earth's  equator  turns,  in  the  diurnal  revolution,  at  the 
rate  of  about  1,000  miles  an  hour  and  ^  of  a  mile  per 
second.  The  motion  around  the  sun,  therefore,  is  nearly 
seventy  times  as  swift  as  the  greatest  motion  around  the 
axis. 


114.  What  is  said  of  the  dimensions  of  the  earth's  orbit  ? 
At  what  rate  does  the  earth  move  in  its  orbit  per  day,  hour, 
minute,  and  second  ?  How  far  does  a  place  on  the  earth's 
equator  move  per  hour  and  second  ?  How  much  swifter  is 
the  motion  in  the  orbit  than  on  its  axis  ? 


84  THE  SUN. 

THE    SEASONS. 

115.  The  change  of  seasons  depends  on  two  causes, 
(1)  the  obliquity  of  the  ecliptic,  and  (2)  the  earth's  axis 
always  remaining  parallel  to  itself.     Had  the  earth's 
axis  been  perpendicular  to  the  plane  of  its  orbit,  the 
equator  would  have  coincided  with  the  ecliptic,  and  the 
sun  would   have  constantly  appeared  in  the  equator 
To  the  inhabitants  of  the  equatorial  regions,  the  sun 
would  always  have  appeared  to  move  in  the  prime  ver- 
tical ;  and  to  the  inhabitants  of  either  pole,  he  would 
always  have  been  in   the  horizon.     But  the  axis  being 
turned  out  of  a  perpendicular  direction   23°   28',  the 
equator  is  turned  the  same  distance  out  of  the  ecliptic ; 
and  since  the  equator  and  ecliptic  are  two  great  circles 
which  cut  each  other  in  two  opposite  points,  the  sun, 
while  performing  his  circuit  in  the  ecliptic,  must  evi- 
dently be  once  a  year  in  each  of  those  points,  and  must 
depart  from  the  equator  of  the  heavens  to  a  distance  on 
either  side  equal  to  the  inclination  of  the  two  circles, 
that  is,  23°  28'. 

116.  The  earth  being  a  globe,  the  sun  constantly  en- 
Kghtens  the  half  next  to  him,*  while  the  other  half  is  in 
darkness.     The  boundary  between  the  enlightened  and 
unenlightened  part,  is  called  the  circle  of  illumination. 
When  the  earth  is  at  one  of  the  equinoxes,  the  sun  is  at 
the  other,  and  the  circle  of  illumination  passes  through 
both  the   Doles.     When  the  earth  reaches  one  of  the 


115.  The  Seasons. — On  what  two  causes  does  the  change 
of  seasons  depend  ?  Had  the  earth's  axis  been  perpendicu- 
lar to  the  plane  of  its  orbit,  in  what  great  circle  would  the  sun 
always  have  appeared  to  move  ? 


*  In  fact,  the  sun  enlightens  a  little  more  than  half  the  earth,  since 
on  account  of  his  vast  magnitude  the  tangents  drawn  from  opposite 
sides  of  the  suit  to  opposite  sides  of  the  earth,  converge  to  a  point 
behind  the  earth,  as  will  be  seen  by  and  by  in  the  representation  of 
eclipses 


THE   SEASONS. 


65 


tropics,  the  sun  being  at  the  other,  the  circle  of  illumin- 
ation cuts  the  earth,  so  as  to  pass  23°  28'  beyond  the 
nearer,  and  the  same  distance  short  of  the  remoter  pole. 
These  results  would  not  be  uniform,  were  not  the  earth's 
axis  always  to  remain  parallel  to  itself.  The  following 
figure  will  illustrate  the  foregoing  statements. 
Fig.  22.  - 


^ 


Let  ABCD  represent  the  earth's  place  in  different 
parts  of  its  orbit,  having  the  sun  in  the  center.     Let  A, 


116.  How  much  of  the  earth  does  the  sun  enlighten  at  once  ? 
Define  the  circle  of  illumination.  How  does  it  cut  the  earth  at 
the  equinoxes  ?  How  at  the  solstices  ?  Explain  figure  22. 
When  the  earth  is  at  one  of  the  tropics  and  the  sun  at  the 
other,  where  is  it  continual  day  and  where  continual  night? 


86  THE  SUN. 

C,  be  the  positions  of  the  earth  at  the  equinoxes,  and  B, 

D,  its  positions  at  the  tropics,  the  axis  ns  being  always 
parallel  to  itself.*     At  A  and  C  the  sun  shines  on  both 
7i  and  s  ;  and  now  let  the  globe  be  turned  round  on  its 
axis,  and  the  learner  will  easily  conceive  that  the  sun 
will  appear  to  describe  the  equator,  which  being  bisected 
by  the  horizon  of  every  place,  of  course  the  day  and 
night  will  be  equal  in  all  parts  of  the  globe.f     Again, 
at  B  when  the  earth  is  at  the  southern  tropic,  the  sun 
shines  23J°  beyond  the  north  pole  n,  and  falls  the  same 
distance  short  of  the  south  pole  s.     The  case  is  exactly 
reversed  when  the  earth  is  at  the  northern  tropic  and 
the  sun  at  the  southern.     While  the  earth  is  at  one  of 
the  tropics,  at  B  for  example,  let  us  conceive  of  it  as  turn- 
ing on  its  axis,  and  we  shall  readily  see  that  all  that  part 
of  the  earth  which  lies  within  the  north  polar  circle  will 
enjoy  continual  day,  while  that  within  the  south  polar 
circle  will  have  continual  night,  and  that  all  other  places 
will  have  their  days  longer  as  they  are  nearer  to  the  en- 
lightened pole,  and  shorter  as  they  are  nearer  to  the  un- 
enlightened pole.     This  figure  likewise  shows  the  suc- 
cessive positions  of  the  earth  at  different  periods  of  the 
year,  with  respect  to  the  signs,  and  what  months  corres- 
pond to  particular  signs.     Thus  the  earth  enters  Libra 
and  the  sun  Aries  on  the  21st  of  March,  and  on  the  21st 
of  June  the  earth  is  just  entering  Capricorn  and  the  sun 
Cancer. 

117.  Had  the  axis  of  the  earth  been  perpendicular 
to  the  plane  of  the  ecliptic,  then  the  sun  would  always 
have  appeared  to  move  in  the  equator,  the  days  would 
every  where  have  been  equal  to  the  nights,  and  there 
could  have  been  no  change  of  seasons.  On  the  other 
hand,  had  the  inclination  of  the  ecliptic  to  the  equator 


*  The  learner  will  remark  that  the  hemisphere  towards  n  is  above, 
and  that  towards  5  is  below  the  plane  of  the  paper.  It  is  important  to 
form  a  just  conception  of  the  position  of  the  axis  with  respect  to  the 
plane  of  its  orbit. 

t  At  the  pole,  the  solar  disk,  at  the  time  of  the  equinox,  appears  bis- 
ected by  the  horizon. 


THE  SEASONS.  87 

been  much  greater  than  it  is,  the  vicissitudes  of  the  yea- 
sons  would  have  been  proportionally  greater  than  at  pres- 
ent. Suppose,  for  instance,  the  equator  had  been  at 
right  angles  to  the  ecliptic,  in  which  case  the  poles  of 
the  earth  would  have  been  situated  in  the  ecliptic  itself; 
then  in  different  parts  of  the  earth  the  appearances 
would  have  been  as  follows.  To  a  spectator  on  the 
equator,  the  sun  as  he  left  the  vernal  equinox  would 
every  day  perform  his  diurnal  revolution  in  a  smaller 
and  smaller  circle,  until  he  reached  the  north  pole,  when 
he  would  halt  for  a  moment,  and  then  wheel  about  and 
return  to  the  equator  in  the  reverse  order.  The  pro- 
gress of  the  sun  through  the  southern  signs,  to  the  south 
pole,  would  be  similar  to  that  already  described.  Such 
would  be  the  appearances  to  an  inhabitant  of  the  equa- 
torial regions.  To  a  spectator  living  in  an  oblique 
sphere,  in  our  own  latitude  for  example,  the  sun  while 
north  of  the  equator  would  advance  continually  north- 
ward, making  his  diurnal  circuits  in  parallels  farther  and 
farther  distant  from  the  equator,  until  he  reached  the 
circle  of  perpetual  apparition,  after  which  he  would 
climb  by  a  spiral  course  to  the  north  star,  and  then  as 
rapidly  return  to  the  equator.  By  a  similar  progress 
southward,  the  sun  would  at  length  pass  the  circle  of 
perpetual  occultation,  and  for  some  time  (which  would 
be  longer  or  shorter  according  to  the  latitude  of  the  place 
of  observation)  there  would  be  continual  night. 

The  great  vicissitudes  of  heat  and  cold  which  would 
attend  such  a  motion  of  the  sun,  would  be  wholly  in- 
compatible with  the  existence  of  either  the  animal  or 
the  vegetable  kingdoms,  and  all  terrestrial  nature  would 


117.  Had  the  earth's  axis  been  perpendicular  to  the  plane 
of  the  ecliptic,  would  there  have  been  any  change  of  seasons  ? 
What  would  have  been  the  consequence  had  the  equator  been 
at  right  angles  to  the  ecliptic  ?  How  would  the  sun  appear  to 
move  to  a  person  on  the  equator  ?  How  to  one  situated  at  the 
pole  ?  How  to  an  inhabitant  of  an  oblique  sphere  ?  How 
would  have  been  the  vicissitudes  of  heat  and  cold  ? 


88 


THE  SUN. 


be  doomed  to  perpetual  sterility  and  desolation.  The 
happy  provision  which  the  Creator  has  made  against 
such  extreme  vicissitudes,  by  confining  the  changes  of 
the  seasons  within  such  narrow  bounds,  conspires  with 
many  other  express  arrangements  in  the  economy  of 
nature  to  secure  the  safety  and  comfort  of  the  human 
race. 

FIGURE  OF  THE  EARTH'S  ORBIT. 

118.  Thus  far  we  have  taken  the  earth's  orbit  as  a 
great  circle,  such  being  the  projection  of  it  on  the  celes- 
tial sphere  ;  but  we  now  proceed  to  .investigate  its  actual 
figure. 

Fig.  23. 


Were  the  earth's  path  a  cii^le,  having  the  sun  in  the 
center,  the  sun  would  always  appear  to  be  at  the  same 


118.  Were  the  earth's  path  a  circle,  how  would  the  distance 
of  the  sun  from  us  always  appear  1  Define  the  radius  vector. 
What  do  we  infer  from  the  fact  that  the  radius  vector  is  con- 
stantly varying  ?  How  do  we  learn  the  relative  distances  ol 
the  earth  ?  How  do  we  construct  a  figure  representing  the 
earth's  orbit  ?  Explain  figure  23. 


89 

distance  from  us ;  that  is,  the  radius  of  its  orbit,  or  ra- 
dius vector,  the  name  given  to  a  line  drawn  from  the 
center  of  the  sun  to  the  orbit  of  any  planet,  would  al- 
ways be  of  the  same  length.  But  the  earth's  distance 
from  the  sun  is  constantly  varying,  which  shows  that 
its  orbit  is  not  a  circle.  We  learn  the  true  figure  of  the 
orbit,  by  ascertaining  the  relative  distances  of  the  earth 
from  the  sun  at  various  periods  of  the  year.  These  all 
being  laid  down  in  a  diagram,  according  to  their  respec- 
tive lengths,  the  extremities,  on  being  connected,  give 
us  our  first  idea  of  the  shape  of  the  orbit,  which  appears 
of  an  oval  form,  and  at  least  resembles  an  ellipse  ;  and, 
on  further  trial,  we  find  that  it  has  the  properties  of  an 
ellipse.  Thus,  let  E  (Fig.  23,)  be  the  place  of  the 
earth,  and  a,  b,  c,  &c.  successive  positions  of  the  sun  ; 
the  relative  lengths  of  the  lines  Ea,  Eft,  &c.  being 
known :  on  connecting  the  points,  a,  b,  c,  &c.  the  result- 
ing figure  indicates  the  true  shape  of  the  earth's  orbit. 

119.  These  relative  distances  are  found  in  two  differ- 
ent ways ;  first,  by  changes  in  the  sun's  apparent  diam- 
eter, and,  secondly,  by  variations  in  his  angular  velo- 
city. The  same  object  appears  to  us  smaller  in  propor- 
tion as  it  is  more  distant ;  and  if  we  see  a  heavenly  body 
varying  in  size  at  different  times,  we  infer  that  it  is  at 
different  distances  from  us  ;  that  when  largest,  it  is  near- 
est to  us,  and  when  smallest,  farthest  off.  Now  when 
the  sun's  diameter  is  measured  accurately  by  instru- 
ments, it  is  found  to  vary  from  day  to  day,  being  when 
greatest  more  than  thirty-two  minutes  and  a  half,  and 
when  smallest  only  thirty-one  minutes  and  a  half,  differ- 
ing in  all,  about  seventy-five  seconds.  When  the  diam- 
eter is  greatest,  which  happens  in  January,  we  know 


119.  How  does  the  same  body  appear  when  at  different  dis- 
tances ?  What  inferences  do  we  make  from  its  variations  of 
size  ?  How  much  does  the  apparent  diameter  of  the  sun  vary 
in  different  parts  of  the  year  ?  When  is  it  greatest,  and 
when  smallest  ?  Define  the  terms  perihelion  and  aphelum. 

8* 


90  THE  SUN. 

that  the  sun  is  nearest  to  us ;  and  when  the  diameter  is 
least,  which  occurs  in  July,  we  infer  that  the  sun  is  at 
the  greatest  distance  from  us. 

The  point  where  the  earth  or  any  planet,  in  its  revo- 
lution, is  nearest  the  sun,  is  called  its  perihelion ;  the 
point  where  it  is  farthest  from  the  sun,  its  aphelion, 

120.  Similar  conclusions  may  be  drawn  from  obser- 
vations on  the  sun's  angular  velocity.  A  body  appears 
to  move  most  rapidly  when  nearest  to  us.  Indeed  the 
apparent  velocity  of  the  sun  increases  rapidly  as  it  ap- 
proaches us,  and  as  rapidly  diminishes  when  it  recedes 
from  us.  If  it  were  to  come  twice  as  near  as  before  it 
would  appear,  to  move  not  merely  twice  as  swift,  but 
four  times  as  swift ;  if  it  came  ten  times  nearer,  its  appa- 
rent velocity  would  be  one  hundred  times  as  great  as 
before.  We  say,  therefore,  that  the  velocity  varies 
inversely  as  the  square  of  the  distance,  for  as  the  dis- 
tance is  diminished  ten  times,  the  velocity  is  increased 
the  square  of  ten,  that  is,  one  hundred  times.  Now  by 
noting  the  time  it  takes  the  sun,  from  day  to  day,  to  re- 
turn to  the  meridian,  we  learn  the  comparative  veloci- 
ties with  which  it  moves  at  different  times,  and  from 
these  we  derive  the  comparative  distances  of  the  sun 
at  the  corresponding  times. 

When  by  either  of  the  foregoing  methods,  we  have 
learned  the  relative  distances  of  the  sun  from  the  earth 
at  various  periods  of  the  year,  we  may  lay  down,  or  plot 
in  a  diagram  like  figure  23,  a  representation  of  the  orbit 
which  the  sun  apparently  describes  about  the  earth,  and 
it  will  give  us  the  figure  of  the  orbit  which  the  earth 
really 'describes  about  the  sun,  in  its  annual  revolution. 


120.  What  conclusions  are  drawn  from  the  variations  in 
the  sun's  angular  velocity  ?  According  to  what  law  does  the 
velocity  vary  1  How  may  we  ascertain  tlic  sun's  daily  rate  ? 
What  great  doctrine  is  it  necessary  to  be  acquainted  with,  in 
order  to  understand  the  celestial  motions  ? 


UNIVERSAL  GRAVITATION.  91 

But  neither  the  revolution  of  the  earth  about  the  sun, 
nor  indeed  that  of  any  of  the  planets,  can  be  well  and 
clearly  understood,  until  we  are  acquainted  with  the 
forces  by  which  their  motions  are  produced,  especially 
with  the  doctrine  of  Universal  Gravitation.  To  this 
subject,  therefore,  let  us  next  apply  our  attention. 


CHAPTER    III. 

OF     UNIVERSAL     GRAVITATION KEPLER's      LAWS MOTION 

IN    AN    ELLIPTICAL    ORBIT PRECESSION    OF    THE    EQUI- 
NOXES. 

121.  WE  discover  in  nature  a  tendency  of  every  por- 
tion of  matter  towards  every  other.  This  tendency  is 
called  gravitation.  In  obedience  to  this  power,  a  stone 
falls  to  the  ground  and  a  planet  revolves  around  the  sun. 

It  was  once  supposed  that  we  could  not  reason  from 
the  phenomena  of  the  earth  to  those  of  the  heavens ; 
since  it  was  held  that  the  laws  of  motion  might  be 
very  different  among  the  heavenly  bodies  from  what 
we  find  them  to  be  on  this  globe  ;  but  Galileo  and  New- 
ton in  their  researches  into  nature,  proceeded  on  the 
idea  that  nature  is  uniform  in  all  her  works,  and  that 
every  where  the  same  causes  produces  the  same  effects, 
and  that  the  same  effects  result  from  the  same  causes. 
That  this  is  a  sound  principle  of  philosophy,  is  proved 
by  the  fact,  that  all  the  conclusions  derived  from  it  in 
the  interpretation  of  nature  are  found  to  be  true.  Hence 
by  studying  the  laws  of  motion  as  exhibited  constantly 
before  our  eyes  in  all  terrestrial  motions,  we  are  learning 


121.  What  force  do  we  observe  in  nature  ?  What  is  this 
force  called  ?  Can  we  reason  from  terrestrial  to  celestial  phe- 
nomena ?  On  what  idea  did  Galileo  and  Newton  proceed  ? 
How  is  this  proved  to  be  a  sound  principle  of  philosophy  I 


92  UNIVERSAL  GRAVITATION. 

the  laws  that  govern  the  movements  of  the  heavenly 
bodies. 

122.  On  the  earth  all  bodies  are  seen  to  fall  towards 
its  center.     A  stone  let  fall  in  any  part  of  the  earth,  de- 
scends immediately  to  the  ground.     This  may  seem  to 
the  young  learner  as  so  much  a  matter  of  course  as  to 
require  no  explanation.     But  stones  fall  in  exactly   op- 
posite directions  on  opposite  sides  of  the  earth,  always 
falling  towards  the  center  of  the  earth  from  every  part 
exterior  to  its  surface ;  as  when  FiS-  24- 

we  hold  a  small  needle  towards 
a  magnetic  ball  or  load  stone,  the 
needle  will  fly  towards  the  ball, 
and  cling  to  its  surface,  to  which- 
ever side  of  the  ball  it  is  present- 
ed. (Fig.  24.)  From  this  uni- 
versal descent  of  bodies  near  the 
earth,  we  infer  the  existence  of 
some  force  which  draws  or  impels  them,  and  this  invisi- 
ble force  we  call  the  attraction  of  gravitation,  or  simply 
gravity. 

123.  By  the  laws  of  gravity  we  mean  the  manner  in 
which  it  always  acts.     They  are  three   in  number,  and 
are  comprehended  in  the  following  proposition : 

Gravity  acts  on  all  matter  alike,  with  a  force  propor- 
tioned to  the  quantity  of  matter,  and  inversely  as  the 
square  of  the  distance. 

First,  gravity  acts  on  all  matter  alike.  Every  body 
in  nature,  whether  great  or  small,  whether  solid,  liquid, 
or  aeriform,  exhibits  the  same  tendency  to  fall  towards 
the  center  of  the  earth.  Some  bodies,  indeed,  seem  less 
prone  to  fall  than  others,  and  some  even  appear  to  rise, 
as  smoke  and  light  vapors.  But  this  is  because  they  are 
supported  by  the  air ;  when  that  is  removed,  they  de- 


1 22.  In  what  directions  do  bodies  fall  in   all  parts  of  the 
earth  ?     Illustrate  by  figure  24.     What  is  gravity  ? 


LAWS  OF  GRAVITY.  93 

scend  alike  towards  the  earth ;  a  guinea  and  a  feather, 
the  lightest  vapor  and  the  heaviest  rocks,  fall  with  equal 
velocities. 

Secondly,  the  force  of  gravity  is  proportioned  to  the 
quantity  of  matter.  A  mass  of  lead  contains  perhaps 
fifty  times  as  much  matter  as  an  equal  bulk  of  cotton  ; 
yet,  if  carried  beyond  the  atmosphere,  and  let  fall  in  ab- 
solute space,  they  would  both  descend  towards  the  earth 
with  equal  speed,  until  they  entered  the  atmosphere, 
and  were  the  atmosphere  removed  they  would  continue 
to  fall  side  by  side  until  they  reached  the  earth.  Now 
if  the  lead  contains  fifty  times  as  much  matter  as  the 
cotton,  it  must  take  fifty  times  the  force  to  make  it  move 
with  equal  velocity.  If  we  double  the  load  we  must 
double  the  team,  If  we  would  continue  to  travel  at  the 
same  speed  as  before.  Hence,  from  the  fact  that  bodies 
of  various  degrees  of  density  descend  alike  towards  the 
center  of  the  earth  by  the  force  of  gravity,  we  infer 
that  that  force  is  always  exerted  upon  bodies  in  exact 
proportion  to  their  quantity  of  matter. 

Thirdly,  the  force  with  which  gravity  acts  upon  bod- 
ies at  different  distances  from  the  earth,  is  inversely  as 
the  square  of  the  distarmz  from  the  center  of  the  earth. 
If  a  pound  of  lead  were  carried  as  far  above  the  earth  as 
from  the  center  to  the  surface  of  the  earth,  it  would 
weigh  only  one-fourth  of  a  pound  ;  for  being  twice  as 
far  as  before  from  the  center  of  the  earth,  its  weight 
would  be  diminished  in  the  proportion  of  the  square  of 
two,  that  is,  four  times. 


123.  What  do  we  mean  by  the  law  of  gravity  ?  State  the 
general  proposition.  Show  that  gravity  acts  on  all  matter  alike. 
How  is  this  consistent  with  the  fact,  that  some  bodies  appear  to 
rise  ?  How  would  all  bodies  fall  in  a  vacuum  ?  Explain  how 
gravity  is  proportioned  to  the  quantity  of  matter.  How  would 
equal  masses  of  lead  and  cotton  fall^if  carried  beyond  the  at- 
mosphere ?  What  do  we  infer  from  the  fact,  that  all  bodies  fall 
towards  the  earth  with  equal  velocities  ?  To  what  is  gravity 
acting  at  different  distances  proportioned  ?  How  much  would 
a  pound  of  lead  weigh,  if  carried  as  far  above  the  earth  as  from 


94  UNIVERSAL  GRAVITATION. 

124.  Bodies  falling  to  the  earth  by  gravity  have  their 
velocity  continually  increased.     For  since  they  retain 
what  motion  they  have  and  constantly  receive  more 
by  the  continued  action  of  gravity,  they  must  move 
faster  and  faster,  as  a  wheel  has  its  velocity  constantly 
accelerated  when  we  continue  to  apply  successive  im 
pulses  to  it. 

The  spaces  which  bodies  describe,  when  falling  freely 
by  gravity,  are  as  the  squares  of  the  times.  It  is  found 
by  experiment,  that  a  body  will  fall  from  a  state  of 
rest  16  j1^  feet  in  one  second.  In  two  seconds  it  wrill  not 
fall  merely  through  double  this  space,  but  through  four 
times  this  space,  that  is,  through  a  distance  expressed 
by  the  square  of  the  time  multiplied  into  16-^.  Conse- 
quently, in  two  seconds  the  fall  will  be  64i,  in  three  se- 
conds 144 J,  and  in  ten  seconds  1608i  feet,  that  is, 
through  one  hundred  times  16^  feet. 

The  weight  of  a  body  is  nothing  more  than  the  ac- 
tion of  gravity  upon  it  tending  to  carry  it  towards  the 
center  of  the  earth.  The  counterpoise  which  is  placed 
in  the  opposite  scale  by  which  its  weight  is  estimated,  is 
the  force  it  takes  to  hold  the  body  back,  which  must  be 
just  equal  to  that  by  which  it  endeavors  to  descend. 

125.  There  is  another  principle  which  it  is  necessary 
clearly  to  comprehend  before  we  can  understand  the  mo- 
tions of  the  heavenly  bodies.     It  is  commonly  called  the 
First  Law  of  Motion  and  is  as  follows : 

Every  body  perseveres  in  a  state  of  rest,  or  of  uniform 
motion  in  a  straight  line,  unless  compelled  by  some  force 
to  change  its  state.  This  law  has  been  fully  established 
by  experiment,  and  is  conformable  to  all  experience. 
It  embraces  several  particulars.  First,  A  body  when  at 


124.  When  a  body  is  falling  towards  the  earth,  how  is  its 
velocity  affected  ?  To  what  are  the  spaces  described  by  fall- 
ing bodies  proportioned  ?  How  far  will  a  body  fall  from  a  state 
of  rest  in  one  second  ?  How  far  in  two  seconds  ?  What  is 
the  weight  of  a  body  ? 


LAWS  OF  MOTION.  95 

rest  remains  so  unless  some  force  puts  it  in  motion ; 
and  hence  it  is  inferred,  when  a  body  is  found  in  mo- 
tion, that  some  force  must  have  been  applied  to  it  suffi- 
cient to  have  caused  its  motion.  Thus,  the  fact  that 
the  earth  is  in  motion  around  the  sun  and  around  its  own 
axis,  is  to  be  accounted  for  by  assigning  to  each  of  these 
motions  a  force  adequate,  both  in  quantity  and  direction, 
to  produce  these  motions  respectively. 

Secondly,  When  a  body  is  once  in  motion  it  will  con- 
tinue to  move  forever,  unless  something  stops  it.  When 
a  ball  is  struck  on  the  surface  of  the  earth,  the  friction 
of  the  earth  and  the  resistance  of  the  air  soon  stop  its 
motion ;  when  struck  on  smooth  ice  it  will  go  much 
farther  before  it  comes  to  a  state  of  rest,  because  the  ice 
opposes  much  less  resistance  than  the  ground ;  and  were 
there  no  impediment  to  its  motion  it  would,  when  once 
set  in  motion,  continue  to  move  without  end.  The 
heavenly  bodies  are  actually  in  this  condition  :  they 
continue  to  move,  not  because  any  new  forces  are  ap- 
plied to  them,  but,  having  been  once  set  in  motion,  they 
continue  in  motion  because  there  is  nothing  to  stop  them. 

Thirdly,  The  motion  to  which  a  body  naturally  tends 
is  uniform  ;  that  is,  the  body  moves  just  as  far  the  se- 
cond minute  as  it  did  the  first,  and  as  far  the  third  as 
the  second,  passing  over  equal  spaces  in  equal  times. 

Fourthly,  A  body  in  motion  will  move  in  a  straight 
line,  unless  diverted  out  of  that  line  by  some  external 
force  ;  and  the  body  will  resume  its  straight  forward  mo- 
tion, when  ever  the  force  that  turns  it  aside  is  with- 
drawn. Every  body  that  is  revolving  in  an  orbit,  like 
the  moon  around  the  earth,  or  the  earth  around  the  sun, 


125.  Recite  the  first  law  of  motion.  How  has  this  law  been 
established  ?  What  does  the  fact,  that  the  earth  is  in  motion 
around  the  sun  imply?  How  would  a  ball  when  once  struck 
continue  to  move,  if  it  rnet  with  no  resistance  ?  Why  do  the 
heavenly  bodies  continue  to  move  ?  What  is  meant  by  saying 
that  motion  is  naturally  uniform  ?  In  what  direction  does 
every  revolving  body  tend  to  move. 


96  UNIVERSAL  GRAVITATION. 

tends  to  move  in  a  straight  line  which  is  a  tangent*  to 
its  orbit. 

Let  us  now  see  how  the  foregoing  principles,  which 
operate  upon  bodies  on  the  earth,  are  extended  so  as  to 
embrace  all  bodies  in  the  universe,  as  in  the  doctrine  of 
Universal  Gravitation.  This  important  principle  is  thus 
defined : 

126.  UNIVERSAL  GRAVITATION,  is  that  influence  by 
which  every  body  in  the  universe,  whether  great  or  small, 
tends  towards  every  other,  with  a  force  which  is  directly 
as  the  quantity  of  matter,  and  inversely  as  the  square  of 
the  distance. 

As  this  force  acts  as  though  bodies  were  drawn  to- 
wards each  other  by  a  mutual  attraction,  the  force  is  de- 
nominated attraction ;  but  ^  it  must  be "  borne  in  mind, 
that  this  term  is  figurative,  and  implies  nothing  respect- 
ing the  nature  of  the  force. 

The  existence  of  such  a  force  in  nature  was  distinctly 
asserted  by  several  astronomers  previous  to  the  time  of 
Sir  Isaac  Newton,  but  its  laws  were  first  promulgated 
by  this  wonderful  man  in  his  Principia,  in  the  year  1687. 
It  is  related,  that  while  sitting  in  a  garden,  and  musing 
on  the  cause  of  the  falling  of  an  apple,  he  reasoned 
thus  :f  that,  since  bodies  far  removed  from  the  earth  fall 
towards  it,  as  from  the  tops  of  towers,  and  the  highest 
mountains,  why  may  not  the  same  influence  extend 
even  to  the  moon ;  and  if  so,  may  not  this  be  the  reason 
why  the  moon  is  made  to  revolve  around  the  earth,  as 
would  be  the  case  with  a  cannon  ball  were  it  projected 
horizontally  near  the  earth  with  a  certain  velocity.  Ac- 
cording to  the  first  law  of  motion,  the  moon,  if  not  con- 
tinually drawn  or  impelled  towards  the  earth  by  some 
force,  would  not  revolve  around  it,  but  would  proceed 
on  in  a  straight  line.  But  going  around  the  earth  as  she 
does,  in  an  orbit  that  is  nearly  circular,  she  must  be 


*  A  tangent  is  a  straight  line  which  touches  a  curve.    Thus  AB  (Fig 
25,)  is  a  tangent  to  the  circle  at  A. 

t  Pemberton's  View  of  Newton's  Philosophy. 


UNIVERSAL  BRAVITATION. 


97 


urged  towards  the  earth  by  some  force,  which  diverts 
her  from  a  straight  course.  For  let  the  earth  (Fig.  25,) 
be  at  E,  and  let  the  arc  described  by  the  moon  in  one 
second  of  time  be  Ab.  Were  the  moon  influenced  by 
no  extraneous  force,  to  turn  aside,  she  would  have  de- 
scribed, not  the  arc  Ab,  but  the  straight  line  AB,  and 
would  have  been  found  at  the  end  of  the  given  time  at 
B  instead  of  b.  She  therefore  departs  from  the  line  in 
which  she  tends  naturally  to  move,  by  the  line  B&, 
which  in  small  angles  may  be  taken  as  equal  to  Aa. 
Fig.  25. 


This  deviation  from  the  tangent  must  be  owing  to  some 
extraneous  force.  Does  this  force  correspond  to  what , 
the  force  of  gravity  exerted  by  the  earth,  would  be  at 
the  distance  of  the  moon  ?  The  question  resolves  itself 
into  this :  Would  the  force  of  gravity  exerted  by  the 
earth  upon  the  moon,  cause  the  moon  to  deviate  from 
her  straight  forward  course  towards  the  earth  just  as 
much  as  she  is  actually  found  to  deviate  ?  Now  we 


126.  Universal  Gravitation. — Define  it.  Why  called  at- 
traction ?  State  the  historical  facts  connected  with  its  discov- 
ery. How  did  Sir  Isaac  Newton  reason  from  the  falling  of  an 
apple  ?  Explain  by  figure  25.  •  How  is  it  proved  that  gravity 
and  no  other  force  causes  the  moon  to  revolve  about  the  earth  ? 

9 


98  UNIVERSAL  GRAVITATION. 

know  how  far  the  moon  is  from  the  earth,  namely,  sixty 
times  as  far  as  it  is  from  the  center  to  the  surface  of  the 
earth  ;  and  since  the  force  of  gravity  decreases  in  pro- 
portion to  the  square  of  the  distance,  this  force  must  be 
3600  times  (which  equals  the  square  of  60,)  less  than  at 
the  surface  of  the  earth.  This  is  found,  on  computa- 
tion, to  be  exactly  the  force  required  to  make  the  moon 
deviate  to  the  amount  she  does  from  the  straight  line  in 
which  she  constantly  tends  to  move  ;  and  hence  it  is 
inferred  that  gravity,  and  no  other  force  than  gravity, 
causes  the  moon  to  circulate  around  the  earth. 

By  this  process  it  was  discovered  that  the  law  of  grav- 
itation extends  to  the  moon.  By  subsequent  inquiries 
it  was  found  to  extend  in  like  manner  to  all  the  planets, 
and  to  every  member  of  the  solar  system ;  and,  finally, 
recent  investigations  have  shown  that  it  extends  to  the 
fixed  stars.  The  law  of  gravitation,  therefore,  is  now 
established  as  the  grand  principle  which  governs  all  the 
motions  of  the  heavenly  bodies. 


127.  There  are  three  great  principles,  according  to 
which  the  motions  of  the  earth  and  all  the  planets 
around  the  sun  are  regulated,  called  Kepler's  Laws,  hav- 
ing been  first  discovered  by  the  great  astronomer  whose 
name  they  bear.  They  may  appear  to  the  young  learner, 
when  he  first  reads  them,  dry  and  obscure  ;  yet  they 
will  be  easily  understood  from  the  explanations  that  fol- 
low ;  and  so  important  have  they  proved  in  astronomical 
inquiries,  that  they  have  acquired  for  their  renowned 
discoverer  the  exalted  appellation  of  the  legislator  of  the 
skies. 

We  will  consider  each  of  these  laws  separately. 


127.  Kepler's  Laws.— Why  so  called  ?     What  appellation 
has  been  given  to  Kepler  ? 


KEPLER  S  LAWS. 


99 


128.  FIRST  LAW.  The  orbits  of  the  earth  and  all  the 
^planets  are  ellipses,  having  the  sun  in  the  common 
focus. 

In  a  circle  all  the  diameters  are  equal  to  each  other ; 
but  if  we  take  a  metallic  wire  or  hoop  and  draw  it  out  on 
opposite  sides,  we  elongate  it  into  an  ellipse,  of  which  the 
different  diameters  are  very  unequal.  That  which  con- 
nects the  two  points  most  distant  from  each  other  is  called 
the  transverse,  and  that  which  is  at  right  angles  to  this 
is  called  the  conjugate  axis.  Thus  AB  (Fig.  26)  is  the 


transverse  axis  and  CD  the  conjugate  of  the  ellipse  AB. 
By  such  a  process  of  elongating  the  circle  into  an  el- 
lipse, the  center  of  the  circle  may  be  conceived  of  as 
drawn  opposite  ways  to  E  and  F,  each  of  which  be- 
comes a  focus,  and  both  together  are  called  the  foci  of  the 
ellipse.  The  distance  GE  or  GF  of  the  focus  from  the 


128.  Recite  the  first  law.  In  a  circle,  how  are  all  the  diam- 
eters ?  How  are  they  in  an  ellipse  ?  What  is  the  longest  di- 
ameter called  ?  What  is  the  shortest  called  ?  Explain  by  figure 
26.  What  is  the  eccentricity  of  the  ellipse  ?  How  many  el- 
lipses may  there  be  having  a  common  focus  ?  Explain  figure 
2§  How  eccentric  is  the  earth's  orbit  ? 


100 


UNIVERSAL  GRAVITATION. 


center  is  called  the  eccentricity  of  the  ellipse  ;  and  the 
ellipse  is  said  to  be  more  or  less  eccentric,  as  the  distance" 
of 'the  focus  from  the  center  is  greater  or  less. 

Now  there  may  be  an  indefinite  number  of  ellipses 
having  one  common  focus,  but  varying  greatly  in  ec- 
centricity. Figure  27  represents  such  a  collection  of 


ellipses  around  the  common  focus  F,  the  innermost  AGD 
having  a  small  eccentricity  or  varying  little  from  a  cir- 
cle; while  the  outermost  ACB  is  a  very  eccentric  ellipse. 
The  orbits  of  all  the  bodies  that  revolve  about  the  sun, 
both  planets  and  comets,  have,  in  like  manner,  a  com- 
mon focus  in  which  the  sun  is  situated,  but  they  differ 
in  eccentricity. 

Most  of  the  planets  have  orbits  of  very  little  eccen- 
tricity, differing  little  from  circles,  but  comets  move  in 
very  eccentric  ellipses. 

The  earth's  path  around  the  sun  varies  so  little  from 
a  circle,  that  a  diagram  representing  it  truly  would 
scarcely  be  distinguished  from  a  perfect  circle  ;  yet 
when  the  comparative  distances  of  the  sun  from  the 
earth  are  taken  at  different  seasons  of  the  year,  as  is  ex- 
plained in  Art.  118,  we  find  that  the  difference  between 


KEPLER'S  LAWS.  101 

the  greatest  and  least  distances  is  no  less  than  3,000,000 
miles. 

129.  SECOND  LAW.     The  radius  vector  of  the  earth, 
or  of  any  planet,  describes  equal  areas  in  equal  times. 

ft  will  be  recollected  that  the  radius  vector  is  a  line 
drawn  from  the  center  of  the  sun  to  a  planet  revolving 
about  the  sun,  (Art.  118.)  Thus  Ea,  Eb,  EC,  (Fig.  23,) 
&c.  are  successive  representations  of  the  radius  vector. 
Now  if  a  planet  sets  out  from  a  and  travels  round  the  sun 
in  the  direction  ofabc,  it  will  move  faster  when  nearer  the 
sun,  as  at  a,  than  when  more  remote  from  it,  as  at  m  ; 
yet  if  ab  and  mn  be  arcs  described  in  equal  times,  then, 
according  to  the  foregoing  law,  the  space  Eab  will  be 
equal  to  the  space  Emn  ;  and  the  same  is  true  of  all  the 
other  spaces  described  in  equal  times.  Although  the 
figure  Eab  is  much  shorter  than  Emn,  yet  its  greater 
breadth  exactly  counterbalances  the  greater  length  oi 
those  figures  which  are  described  by  the  radius  vector 
where  it  is  longer. 

130.  THIRD  LAW.     The  squares  of  the  periodical  times 
are  as  the  cubes  of  the  mean  distances  from  the  sun. 

The  periodical  time  of  a  body  is  the  time  it  takes  to 
complete  its  orbit  in  its  revolution  about  the  sun.  Thus 
the  earth's  periodic  time  is  one  year,  and  that  of  the 
planet  Jupiter  is  about  twelve  years.  As  Jupiter  takes 
so  much  longer  time  to  travel  round  the  sun  than  the 
earth  does,  we  might  suspect  that  his  orbit  was  larger 
than  that  of  the  earth,  and  of  course  that  he  was  at 
a  greater  distance  from  the  sun,  and  our  first  thought 
might  be  that  he  was  probably  twelve  times  as  far  off; 
but  Kepler  discovered  that  the  distances  did  not  increase 
as  fast  as  the  times  increased,  but  that  the  planets  which 


129.  State  Kepler's  second  law.   Explain  by  figure  23,  p.  88. 

130.  State  Kepler's  third  law.     What  is  meant  by  the  peri- 
odical time  of  a  body  ?     Do  planets  jnove  faster  or  slower  as 
they  are  more  distant  from  the  sun  ?     Explain  the  law. 

9* 


102  UNIVERSAL  GRAVITATION. 

are  more  distant  from  the  sun  actually  move  slower  than 
those  which  are  nearer.  After  trying  a  great  many  pro- 
portions, he  at  length  found  that  if  we  take  the  squares 
of  the  periodic  times  of  two  planets,  the  greater  square 
contains  the  less,  just  as  often  as  the  cube  of  the  dis 
tance  of  the  greater  contains  that  of  the  less.  This  fact 
is  expressed  by  saying,  that  the  squares  of  the  periodic 
times  are  to  one  another  as  the  cubes  of  the  distances. 
This  law  is  of  great  use  in  determining  the  distances 
of  all  the  planets  from  the  sun,  as  we  shall  see  more  fully 
hereafter. 

MOTION  IN  AN  ELLIPTICAL  ORBIT. 

131.  Let  us  now  endeavor  to  gain  a  just  conception 
of  the  forces  by  which  the  earth  and  all  the  planets  are 
made  to  revolve  about  the  sun. 

In  obedience  to  the  first  law  of  motion,  every  moving 
body  tends  to  move  in  a  straight  line  ;  and  were  not  the 
planets  deflected  continually  towards  the*  sun  by  the 
force  of  attraction,  these  bodies  as  well  as  others  would 
move  forward  in  a  rectilineal  direction.  We  call  the  force 
by  which  they  tend  to  such  a  direction  the  projectile 
force,  because  its  effects  are  the  same  as  though  the  body 
were  originally  projected  from  a  certain  point  in  a  certain 
direction.  It  is  an  interesting  problem  for  mechanics  to 
solve,  what  was  the  nature  of  the  impulse  originally 
given  to  the  earth,  in  order  to  impress  upon  it  its  two 
motions,  the  one  around  its  own  axis,  the  other  around 
the  sun.  If  struck  in  the  direction  of  its  center  of 
gravity  it  might  receive  a  forward  motion,  but  no  rota- 
tion on  its  axis.  It  must,  therefore,  have  been  impelled 
by  a  force,  whose  direction  did  not  pass  through  its 


131.  Explain  how  a  body  is  made  to  revolve  in  an  orbit, 
under  the  action  of  two  forces.  What  is  meant  by  the  projec- 
tile force  ?  How  must  the  earth  have  been  impelled  in  order 
to  receive  its  present  motions  ?  How  illustrated  by  the  mo- 
tions of  a  top  7 


MOTION  IN  AN   ELLIPTICAL  ORBIT.  103 

center  of  gravity.  Bernoulli!,  a  celebrated  mathemati- 
cian, has  calculated  that  the  impulse  must  have  been 
given  very  nearly  in  the  direction  of  the  center,  the 
point  of  projection  being  only  the  165th  part  of  the 
earth's  radius  from  the  center.  This  impulse  alone 
would  cause  the  earth  to  move  in  a  right  line  :  gravita- 
tion towards  the  sun  causes  it  to  describe  an  orbit. 
Thus  a  top  spinning  on  a  smooth  plane,  as  that  of  glass 
or  ice,  impelled  in  a  direction  not  coinciding  with  that 
of  the  center  of  gravity,  may  be  made  to  imitate  the  two 
motions  of  the  earth,  especially  if  the  experiment  is  tried 
in  a  concave  surface  like  that  of  a  large  bowl.  The  re- 
sistance occasioned  by  the  surface  on  which  the  top 
moves,  and  that  of  the  air,  will  gradually  destroy  the 
force  of  projection  and  cause  the  top  to  revolve  in  a 
smaller  and  smaller  orbit ;  but  the  earth  meets  with  no 
such  resistance,  and  therefore  makes  both  her  days  and 
years  of  the  same  length  from  age  to  age.  A  body, 
therefore,  revolving  in  an  orbit  about  a  center  of  attrac- 
tion, is  constantly  under  the  influence  of  two  forces, — 
the  projectile  force,  which  tends  to  carry  it  forward  in  a 
straight  line  which  is  a  tangent  to  its  orbit,  and  the  cen- 
tripetal force,  by  which  it  tends  towards  the  center. 

132.  As  an  example  of  a  body  revolving  in  an  orbit 
under  the  influence  of  two  forces,  suppose  a  body  pla- 
ced at  any  point  P  (Fig.  28,)  above  the  surface  of  the 
earth,  and  let  PA  be  the  direction  of  the  earth's  center. 
If  the  body  were  allowed  to  move  without  receiving 
any  impulse,  it  would  descend  to  the  earth  in  the  direc- 
tion PA  with  an  accelerated  motion.  But  suppose  that 
at  the  moment  of  its  departure  from  P,  it  receives  an 
impulse  in  the  direction  PB,  which  would  carry  it  to  B 
in  the  time  the  body  would  fall  from  P  to  A ;  then  un- 
der the  influence  of  both  forces  it  would  descend  along 
the  curve  PD.  If  a  stronger  impulse  were  given  it  in 


132.  Explain  figure  28.     How  might  a  body  be  made  to 
circulate  quite  around  the  earth  ? 


104 


UNIVERSAL  GRAVITATION. 


the  direction  PB,  it  would  describe  a  larger  curve  PE, 
or  PF,  or  finally,  it  would  go  quite  round  the  earth  and 
return  again  to  P. 

133.  The  most  simple  example  we  have  of  the  com- 
bined action  of  these  two  forces,  is  the  motion  of  a  mis- 
sile thrown  from  the  hand,  or  of  a  ball  fired  from  a  can- 
non. It  is  well  known  that  the  particular  form  of  the 
curve  described  by  the  projectile,  in  either  case,  will  de- 
pend upon  the  velocity  with  which  it  is  thrown.  In 
each  case  the  body  will  begin  to  move  in  the  line  of  di- 
rection in  which  it  is  projected,  but  it  will  soon  be  de- 
flected from  that  line  towards  the  earth.  It  will  how- 
ever continue  nearer  to  the  line  of  projection  as  the  ve- 

Fig.  29. 


locity  of  projection  is  greater.     Thus  let  AB  (Fig.  29,) 


133.  When  a  cannon  ball  is  fired  with  different  velocities, 
•when  is  its  motion  nearest  to  the  line  of  projection  ? 


MOTION   IN  AN  ELLIPTICAL   ORBIT. 


105 


perpendicular  to  AC  represent  the  line  of  projection. 
The  body  will,  in  every  case,  commence  its  motion  in 
the  line  AB,  which  will  therefore  be  the  tangent  to  the 
curve  it  describes  ;  but  if  it  be  thrown  with  a  small  ve- 
'ocity,  it  will  soon  depart  from  the  tangent,  describing 
the  line  AD ;  with  a  greater  velocity  it  will  describe  a 


curve  nearer  to  the  tangent,  as  AE ;    and  with 
greater  velocity  it  will  describe  the  curve  AF. 


still 


134.  In  figure  30,  suppose  the  planet  to  have  passed 
the  point  C  with  so  small  a  velocity,  that  the  attraction 
of  the  sun  bends  its  path  very  much,  and  causes  it  im- 
mediately to  begin  to  approach  towards  the  sun ;  the 
sun's  attraction  will  increase  its  velocity  as  it  moves 
through  D,  E,  and  F.  For  the  sun's  attractive  force  on 


the  planet,  when  at  D,  is  acting  in  the  direction  DS, 
and,  on  account  of  the  small  inclination  of  DE  to  DS, 
the  force  acting  in  the  line  DS  helps  the  planet  forward 
in  the  path  DE,  and  thus  increases  its  velocity.  In  like 
manner,  the  velocity  of  the  planet  will  be  continually 
increasing  as  it  passes  through  E,  and  F ;  and  though 


134.  Explain  the  motion  of  a  planet  in  an  elliptical  orbit, 
from  figure  30. 


UNIVERSAL  GRAVITATION. 

the  attractive  force,  on  account  of  the  planet's  nearness, 
is  much  increased,  and  tends  therefore  to  make  the 
orbit  more  curved,  yet  the  velocity  is  also  so  much  in- 
creased that  the  orbit  is  not  more  curved  than  before. 
The  same  increase  of  velocity  occasioned  by  the  planet' s 
approach  to  the  sun,  produces  a  greater  increase  of  cen- 
trifugal force  which  carries  it  off  again.  We  may  see 
also  why,  when  the  planet  has  reached  the  most  distant 
parts  of  its  orbit,  it  does  not  entirely  fly  off,  and  never 
return  to  the  sun.  For  when  the  planet  passes  along 
H,  K,  A,  the  sun's  attraction  retards  the  planet,  just  as 
gravity  retards  a  ball  rolled  up  hill ;  and  when  it  has 
reached  C,  its  velocity  is  very  small,  and  the  attraction 
at  the  center  of  force  causes  a  great  deflection  from  the 
tangent,  sufficient  to  give  its  orbit  a  great  curvature, 
and  the  planet  turns  about,  returns  to  the  sun,  and  goes 
over  the  same  orbit  again.  As  the  planet  recedes  from 
the  sun,  its  centrifugal  force  diminishes  faster  than  the 
force  of  gravity,  so  that  the  latter  finally  preponderates. 

135.  We  may  imitate  the  motion  of  a  body  in  its  orbit 
by  suspending  a  small  ball  from  the  ceiling  by  a  long  string. 
The  ball  being  drawn  out  of  its  place  of  rest,  (which  is 
directly  under  the  point  of  suspension,)  it  will  tend  con- 
stantly towards  the  same  place  by  a  force  which  corres- 
ponds to  the  force  of  attraction  of  a  central  body.  If 
an  assistant  stands  under  the  point  of  suspension,  his 
head  occupying  the  place  of  the  ball  when  at  rest,  the 
ball  may  be  made  to  revolve  about  his  head  as  the  earth 
or  any  planet  revolves  about  the  sun.  By  projecting  the 
ball  in  different  directions,  and  with  different  degrees  of 
velocity,  we  may  make  it  describe  different  orbits,  ex- 
emplifying principles  which  have  been  explained  in  the 
foregoing  articles. 


135.  How  may  we  imitate  the  motion  of  a  body  in  its  or- 
bit ?     How  may  we  make  the  ball  describe  different  orbits  ? 


- 

PRECESSION  OF  THE  EQUINOXES.  107 

PRECESSION  OF  THE  EQUINOXES. 

136  THE  PRECESSION  OF  THE  EQUINOXES,  is  a  slow 
but  continual  shifting  of  the  equinoctial  points  from  east 
to  west. 

Suppose  that  we  mark  the  exact  place  in  the  heavens 
where,  during  the  present  year,  the  sun  crosses  the  equa- 
tor, and  that  this  point  is  close  to  a  certain  star  ;  next 
year  the  sun  will  cross  the  equator  a  little  way  west- 
ward of  that  star,  and  thus  every  year  a  little  farther  west- 
ward, so  that  in  a  long  course  of  ages,  the  place  of  the 
equinox  will  occupy  successively  every  part  of  the  eclip- 
tic, until  we  come  round  to  the  same  star  again.  As, 
therefore,  the  sun,  revolving  from  west  to  east  in  his  ap- 
parent orbit,  comes  round  towards  the  point  where  it 
left  the  equinox,  it  meets  the  equinox  before  it  reaches 
that  point.  The  appearance  is  as  though  the  equinox 
goes  forward  to  meet  the  sun,  and  hence  the  phenome- 
non is  called  the  Precession  of  the  Equinoxes,  and  the 
fact  is  expressed  by  saying  that  the  equinoxes  retrograde 
on  the  ecliptic,  until  the  line  of  the  equinoxes  makes  a 
complete  revolution  from  east  to  west.  The  equator  is 
conceived  as  sliding  westward  on  the  ecliptic,  always 
preserving  the  same  inclination  to  it,  as  a  ring  placed  at 
a  small  angle  with  another  of  nearly  the  same  size, 
which  remains  fixed,  may  be  slid  quite  around  it,  giving 
a  corresponding  motion  to  the  two  points  of  intersec- 
tion. It  must  be  observed,  however,  that  this  mode  of 
conceiving  of  the  precession  of  the  equinoxes  is  purely 
imaginary,  and  is  employed  merely  for  the  convenience 
of  representation. 

137.  The  amount  of  precession  annually  is  50. "1  ; 
whence,  since  there  are  3600"  in  a  degree,  and  360°  in 


136.  Precession  of  the  Equinoxes. — Define  it.  If  the  sun 
crosses  the  equator  near  a  certain  star  this  year,  where  will  it 
cross  it  next  year  ?  Why  is  the  fact  called  the  precession  of 
the  equinoxes  1  How  is  the  equator  conceived  as  moving 
with  regard  to  the  ecliptic  ? 


108  UNIVERSAL  GRAVITATION. 

the  whole  circumference,  and  consequently,  1296000", 
this  sum  divided  by  50.1  gives  25868  years  for  the  pe- 
riod of  a  complete  revolution  of  the  equinoxes. 

138.  Suppose  now  we  fix  to  the  center  of  each  of  the 
two  rings,  (Art.  136,)  a  wire  representing  its  axis,  one 
corresponding  to  the  axis  of  the  ecliptic,  the  other  to 
that  of  the  equator,  the  extremity  of  each  being  the  pole 
of  its  circle.  As  the  ring  denoting  the  equator  turns 
round  on  the  ecliptic,  which  with  its  axis  remains  fixed, 
it  is  easy  to  conceive  that  the  axis  of  the  equator  re- 
volves around  that  of  the  ecliptic,  and  the  pole  of  the 
equator  around  the  pole  of  the  ecliptic,  and  constantly  at 
a  distance  equal  to  the  inclination  of  the  two  circles.  To 
transfer  our  conceptions  to  the  celestial  sphere,  we  may 
easily  see  that  the  axis  of  the  diurnal  sphere,  (that  of 
the  earth  produced,  Art.  15,)  would  not  have  its  pole 
constantly  in  the  same  place  among  the  stars,  but  that 
this  pole  would  perform  a  slow  revolution  around  the 
pole  of  the  ecliptic  from  east  to  west,  completing  the  cir- 
cuit in  about  26,000  years.  Hence  the  star  which  we 
now  call  the  pole  star,  has  not  always  enjoyed  that  dis- 
tinction, nor  will  it  always  enjoy  it  hereafter.  When 
the  earliest  catalogues  of  the  stars  were  made,  this  star 
was  12°  from  the  pole.  It  is  now  1°  33',  and  will  ap- 
proach still  nearer  ;  or  to  speak  more  accurately,  the  pole 
will  come  still  nearer  to  this  star,  after  which  it  will 
leave  it,  and  successively  pass  by  others.  In  about 
13,000  years,  the  bright  star  «  Lyrse,  which  lies  on  the 
circle  of  revolution  opposite  to  the  present  pole  star, 


137.  What  is  the  amount  of  precession  annually?    In  what 
time  will  the  equinoxes  perform  a  complete  revolution  ? 

138.  Illustrate  the  precession  of  the  equinoxes  by  an  appa- 
ratus of  wires.     How  is  the  pole  of  the  earth  situated  with 
respect  to  the  stars  at  different  times?     Has  the  present  pole 
star  always  been  such  ?     What  will  be  the  pole  star  13,000 
years  hence  ?     Will  this  cause   affect  the  elevation  of  tho 
north  pole  above  the  horizon  ? 


PRECESSION  OF  THE  EQUINOXES.  109 

will  be  within  5°  of  the  pole,  and  will  constitute  the 
Pole  Star.  As  a  Lyrae  now  passes  near  our  zenith,  the 
learner  might  suppose  that  the  change  of  position  of  the 
pole  among  the  stars,  would  be  attended  with  a  change 
of  altitude  of  the  north  pole  above  the  horizon.  This 
mistaken  idea  is  one  of  the  many  misapprehensions 
which  result  from  the  habit  of  considering  the  horizon 
as  a  fixed  circle  in  space.  However  the  pole  might 
shift  its  position  in  space,  we  should  still  be  at  the 
same  distance  from  it,  and  our  horizon  would  always 
reach  the  same  distance  beyond  it. 

139.  The  time  occupied  by  the  sun  in  passing  from 
the  equinoctial  point  round  to  the  same  point  again,  is 
called  the  TROPICAL  YEAR.  As  the  sun  does  not  perform 
a  complete  revolution  in  this  interval  but  falls  short  of  it 
50."  1,  the  tropical  year  is  shorter  than  the  sidereal  by 
20m.  20s.  in  mean  solar  time,  this  being  the  time  of  de- 
scribing an  arc  of  50."1  in  the  annual  revolution.*  The 
changes  produced  by  the  precession  of  the  equinoxes  in 
the  apparent  places  of  the  circumpolar  stars,  have  led  to 
some  interesting  results  in  chronology.  In  consequence 
of  the  retrograde  motion  of  the  equinoctial  points,  the 
signs  of  the  ecliptic,  do  not  correspond  at  present  to 
the  constellations  which  bear  the  same  names,  but  lie 
about  one  whole  sign  or  30°  westward  of  them.  Thus, 
that  division  of  the  ecliptic  which  is  called  the  sign 
Taurus,  lies  in  the  constellation  Aries,  and  the  sign 
Gemini  in  the  constellation  Taurus.  Undoubtedly  how- 
ever when  the  ecliptic  was  thus  first  divided,  and  the 
divisions  named,  the  several  constellations  lay  in  the  re- 
spective divisions  which  bear  their  names.  How  long 
is  it,  then,  since  our  zodiac  was  formed  ? 


139.  Define  the  tropical  year.  How  much  shorter  is  the 
tropical  than  the  sidereal  year  ?  How  has  the  precessio»of  the 
equinoxes  been  applied  in  Chronology  ? 

*  59'  8."3  :  24h.  :  :  50."1  :  20m.  20s. 
10 


110  THE  MOON. 

50."1  :  1  year:  :30°(~  108000")  :  2155.6  years. 
The  result  indicates  that  the  present  divisions  of  the 
zodiac,  were  made  soon  after  the  establishment  of  the 
Alexandrian  school  of  astronomy. 


CHAPTER    IV. 

OF  THE  MOON  -  PHASES  -  REVOLUTIONS. 

140.  NEXT  to  the  Sun  the  Moon  naturally  claims  our 
attention.     She  is  an  attendant  or  satellite  to  the  earth, 
araund  which  she   revolves  at  the  distance  of  nearly 
240,000  miles,  or  more  exactly  238,545   miles.      Her 
angular  diameter  is  about  half  a  degree,  and  her  real  diam- 
eter 2160  miles.     She  is  therefore  a  comparatively  small 
body,  being  only  one  forty-ninth  part  as  large  as  the 
earth. 

The  moon  shines  by  reflected  light  borrowed  from 
the  sun,  and  when  full  exhibits  a  disk  of  silvery  bright- 
ness, diversified  by  extensive  portions  partially  shaded. 
These  dusky  spots  are  generally  said  to  be  land,  and  the 
brighter  parts  water  ;  but  astronomers  tell  us  that  if  ei- 
ther are  water,  it  must  be  the  darker  portions.  Land  by 
scattering  the  rays  of  the  sun's  light  would  appear  more 
luminous  than  the  ocean  which  reflects  the  light  like  a 
mirror.  By  the  aid  of  the  telescope,  we  see  undoubted 
signs  of  a  varied  surface,  in  some  parts  composed  of  ex- 
tensive tracts  of  level  country,  and  in  others  exceedingly 
broken  by  mountains  and  valleys. 

141.  The  line  which  separates  the  enlightened  from 
the  dark  portions  of  the  moon's  disk,  is  called  the  Ter- 


140.  The  Moon. — What  relation  has  the  moon  to  the  earth  ? 
State  her  distance,  diameter  and  bulk.  Is  her  light  direct  or 
reflected  ?  What  are  the  dark  places  in  the  moon  generally  un- 
derstood to  be  ?  Why  would  water  appear  darker  than  land  ? 
What  does  the  telescope  reveal  to  us  respecting  the  moon  ? 


LUNAR  GEOGRAPHY.  Ill 

minator.  (See  Frontispiece.)  As  the  terminator  traver- 
ses the  disk  from  new  to  full  moon,  it  appears  through  the 
telescope  exceedingly  broken  in  some  parts^but  smooth 
in  others,  indicating  that  portions  of  the  lunar  surface  are 
uneven  while  others  are  level.  The  broken  regions  ap- 
pear brighter  than  the  smooth  tracts.  The  latter  have 
been  taken  for  seas,  but  it  is  supposed  with  more  prob- 
ability that  they  are  extensive  plains,  since  they  are  still 
too  uneven  for  the  perfect  level  assumed  by  bodies  of 
water.  That  there  are  mountains  in  the  moon,  is  known 
by  several  distinct  indications.  First,  when  the  moon 
is  increasing,  certain  spots  are  illuminated  sooner  than 
the  neighboring  places,  appearing  like  bright  points  be- 
yond the  terminator,  within  the  dark  part  of  the  disk, 
in  the  same  manner  as  the  tops  of  mountains  on  the 
earth  are  tipped  with  the  light  of  the  sun,  in  the  morn- 
ing, while  the  regions  below  are  still  dark.  Secondly, 
after  the  terminator  has  passed  over  them,  they  project 
shadows  upon  the  illuminated  part  of  the  disk,  always 
opposite  to  the  sun,  corresponding  in  shape  to  the  form 
of  the  mountain,  and  undergoing  changes  in  length  from 
night  to  night,  according  as  the  sun  shines  upon  that 
part  of  the  moon  more  or  less  obliquely.  Many  indi- 
vidual mountains  rise  to  a  great  height  in  the  midst  of 
plains,  and  there  are  several  very  remarkable  mountain- 
ous groups,  extending  from  a  common  center  in  long 
chains. 

142.  That  there  are  also  valleys  in  the  moon,  is 
equally  evident.  The  valleys  are  known  to  be  truly 
such,  particularly  by  the  manner  in  which  the  light  of 
the  sun  falls  upon  them,  illuminating  the  part  opposite 
to  the  sun  while  the  part  adjacent  is  dark,  as  is  the  case 
when  the  light  of  a  lamp  shines  obliquely  into  a  china 


141.  Define  the  terminator.     What  do  we  learn  from  its  rug- 
ged appearance  ?     State  the  proofs  of  mountains  in  the  moon. 

142.  State  the  proofs  of  valleys  in  the  moon.     When  is  the 
best  time  for  viewing  the  mountains  and  valleys  of  the  moon. 


112  THE    MOON. 

cup.  These  valleys  are  often  remarkably  regular,  and 
some  of  them  almost  perfect  circles.  In  several  instan- 
ces, a  circular  chain  of  mountains  surrounds  an  exten- 
sive valley,  which  appears  nearly  level,  except  that  a 
sharp  mountain  sometimes  rises  from  the  center.  The 
best  time  for  observing  these  appearances  is  near  the 
first  quarter  of  the  moon,  when  half  the  disk  is  en- 
lightened ;*  but  in  studying  the  lunar  geography,  it  is 
expedient  to  observe  the  moon  every  evening  from  new 
to  full,  or  rather  through  her  entire  series  of  changes. 

143.  The  various  places  on  the  moon's  disk  have  re- 
ceived appropriate  names.  The  dusky  regions,  being 
formerly  supposed  to  be  seas,  were  named  accordingly ; 
and  other  remarkable  places  have  each  two  names,  one 
derived  from  some  well  known  spot  on  the  earth,  and 
the  other  from  some  distinguished  personage.  Thus 
the  same  bright  spot  on  the  surface  of  the  moon  is 
called  Mount  Sinai  or  Tycho,  and  another.  Mount  Et- 
na or  Copernicus.  The  names  of  individuals,  how- 
ever, are  more  used  than  the  others.  The  frontispiece 
exhibits  the  telescopic  appearance  of  the  full  moon.  A 
few  of  the  most  remarkable  points  have  the  following 
names,  corresponding  to  the  numbers  and  letters  on  the 
map.  (See  Frontispiece.) 

1.  Tycho,  A.  Mare  Humorum, 

2.  Kepler,  B.  Mare  Nubium, 

3.  Copernicus,  C.  Mare  Imbrium, 

4.  AHstarchus,  D.  Mare  Nectaris, 

5.  Helicon,  E.  Mare  Tranquilitatis, 

6.  Eratosthenes,          F.  Mare  Serenitatis, 

7.  Plato,  G.  Mare  Fecunditatis, 

8.  Archimedes,  H.  Mare  Crisium, 

9.  Eudoxus, 
10.  Aristotle, 


*  It  is  earnestly  recommended  to  the  student  of  astronomy,  to  exam- 
ine the  moon  repeatedly  with  the  best  telescope  he  can  command,  using 
low  powers  at  first,  for  the  sake  of  a  better  light 


LUNAR  GEOGRAPHY.  113 

The  frontispiece  represents  the  appearance  of  the 
moon  in  the  telescope  when  full  and  when  five  days 
old.  In  the  latter  cut,  the  learner  will  remark  the  rough, 
rugged  appearance  of  the  terminator ;  the  illuminated 
points  beyond  the  terminator  within  the  dark  part  of  the 
moon,  which  are  the  tops  of  mountains ;  and  the  nu- 
merous circular  spaces,  which  exhibit  valleys  or  caverns 
surrounded  by  mountainous  chains.  Those  circles  which 
are  near  the  terminator  into  which  the  sun's  light  shines 
very  obliquely,  cast  deep  shadows  on  the  sides  opposite 
the  sun.  Those  more  remote  from  the  terminator,  and 
farther  within  the  illuminated  part  of  the  moon,  into 
which  the  sun  shines  more  directly,  have  a  greater  por- 
tion illuminated,  with  shorter  shadows  ;  and  those  which 
lie  near  the  edge  of  the  moon,  most  distant  from  the  ter 
minator,  are  of  an  oval  figure,  being  presented  obliquely 
to  the  eye. 

144.  The  heights  of  the  lunar  mountains,  and  the 
depths  of  the  valleys,  can  be  estimated  with  a  considera- 
ble degree  of  accuracy.  Some  of  the  mountains  are  as 
high  as  five  miles,  and  the  valleys  in  some  instances 
are  four  miles  deep.  Hence  it  is  inferred  that  the  sur- 
face of  the  moon  is  more  broken  and  irregular  than  that 
of  the  earth,  its  mountains  being  higher  and  its  valleys 
deeper  in  proportion  to  its  magnitude  than  that  of  the 
earth:  The  lunar  mountains  in  general,  exhibit  an  ar- 


143.  How  are  places  in  the  moon  named  ?     Point-  out  the 
most  remarkable  places  on  the  map  of  the  full  moon.     Point 
out  the  mountains,  valleys,  and  craters,  on  the  cut,  which  rep- 
resents the  moon  five  days  old. 

144.  Specify  the  heights  of  some  of  the  lunar  mountains. 
Is  the  surface  of  the  moon  more  or  less  broken  than  that  of  the 
earth  ?     Are  the  mountains  like  or  unlike  ours  ?     What  is  the 
first  variety  ?     What  is  the  shape  of  the  insulated  mountains  ? 
How  can  their  heights  be  calculated  ?     What  is  said  of  the 
second  variety,  the  mountain  ranges  ?     What  .is  said  of  the 
circular  ranges  ?     What  is  said  of  the  central  mountains  ? 

10* 


114  THE  MOON. 

rangement  and  an  aspect  very  different  from  the  moun- 
tain scenery  of  our  globe.  They  may  be  arranged  un- 
der the  four  following  varieties. 

First,  Insulated  Mountains,  which  rise  from  plains 
nearly  level,  shaped  like  a  sugar  loaf,  which  may  be, 
supposed  to  present  an  appearance  somewhat  similar  to 
Mount  Etna,  or  the  Peak  of  TenerifFe.  The  shadows 
of  these  mountains,  in  certain  phases  of  the  moon,  are 
as  distinctly  perceived,  as  the  shadow  of  an  upright  staff, 
when  placed  opposite  to  the  sun  ;  and  these  heights  can 
be  calculated  from  the  length  of  their  shadows.  Some 
of  these  mountains  being  elevated  in  the  midst  of  exten- 
sive plains,  would  present  to  a  spectator  on  their  sum- 
mits, magnificent  views  of  the  surrounding  regions. 

Secondly,  Mountain  Ranges,  extending  in  length  two 
or  three  hundred  miles.  These  ranges  bear  a  distant  re- 
semblance to  our  Alps,  Appenines,  and  Andes ;  but  they 
are  much  less  in  extent.  Some  of  them  appear  very 
rugged  and  precipitous,  and  the  highest  ranges  are  in 
some  places  more  than  four  miles  in  perpendicular  alti- 
tude. In  some  instances,  they  are  nearly  in  a  straight 
line  from  northeast  to  southwest,  as  in  that  range  called 
the  Appenines ;  in  other  cases  they  assume  the  form  of 
a  semicircle  or  crescent. 

Thirdly,  Circular  Ranges,  which  appear  on  almost 
every  part  of  the  moon's  surface,  particularly  in  its  south- 
ern regions.  This  is  one  grand  peculiarity  of  the  lunar 
ranges,  to  which  we  have  nothing  similar  on  the  earth. 
A  plain,  and  sometimes  a  large  cavity,  is  surrounded 
with  a  circular  ridge  of  mountains,  which  encompasses 
it  like  a  mighty  rampart.  These  annular  ridges  and 
plains  are  of  all  dimensions,  from  a  mile  to  forty  or  fifty 
miles  in  diameter,  and  are  to  be  seen  in  great  numbers 
over  every  region  of  the  moon's  surface  ;  they  are  most 
conspicuous,  however,  near  the  upper  and  lower  limbs 
about  the  time  of  half  moon. 

The  mountains  which  form  these  circular  ridges  are 
of  different  elevations,  from  one  fifth  of  a  mile  to  three 
and  a  half  miles,  and  their  shadows  cover  one  half  of 
the  plain  at  the  base.  These  plains  are  sometimes  on 


LUNAR   GEOGRAPHY.  115 

a  level  with  the  general  surface  of  the  moon,  and  in 
other  cases  they  are  sunk  a  mile  or  more  below  the  level 
of  the  ground,  which  surrounds  the  exterior  circle  of  the 
mountains. 

Fourthly,  Central  Mountains,  or  those  which  are 
placed  in  the  middle  of  circular  plains.  In  many  of  the 
plains  and  cavities  surrounded  by  circular  ranges  cf 
mountains  there  stands  a  single  insulated  mountain, 
which  rises  from  the  center  of  the  plain,  and  whose 
shadow  sometimes  extends  in  the  form  of  a  pyramid 
half  across  the  plain  or  more  to  the  opposite  ridges. 
These  central  mountains  are  generally  from  half  a  mile 
to  a  mile  and  a  half  in  perpendicular  altitude.  In  some 
instances  they  have  two  and  sometimes  three  different 
tops,  wThose  shadows  can  be  easily  distinguished  from 
each  other.  Sometimes  they  are  situated  towards  one 
side  of  the  plain  or  cavity,  but,  in  the  great  majority 
of  instances,  their  position  is  nearly  or  exactly  central. 
The  lengths  of  their  bases  vary  from  five  to  about  fifteen 
or  sixteen  miles. 

145.  The  Lunar  Caverns  form  a  very  peculiar  and 
prominent  feature  of  the  moon's  surface,  and  are  to 
be  seen  throughout  almost  every  region,  but  are  most 
numerous  in  the  southwest  part  of  the  moon.  Nearly  a 
hundred  of  them,  great  and  small,  may  be  distinguished 
in  that  quarter.  They  are  all  nearly  of  a  circular  shape, 
and  appear  like  a  very  shallow  egg-cup.  The  smaller 
cavities  appear  within  almost  like  a  hollow  cone,  with 
the  sides  tapering  towards  the  center ;  but  the  larger 
ones  have  for  the  most  part,  flat  bottoms,  from  the  cen- 
ter of  which  there  frequently  rises  a  small  steep  conical 
hill,  which  gives  them  a  resemblance  to  the  circular 
ridges^ and  central  mountains  before  described.  In  some 
instances  their  margins  are  level  with  the  general  sur 
face  of  the  moon,  but  in  most  cases  they  are  encircled 


145.  Lunar  Caverns. — What  is  said  of  their  number,  shapo 
and  appearances  ? 


116  THE  MOON. 

with  a  high  annular  ridge  of  mountains,  marked  with 
lofty  peaks.  Some  of  the  larger  of  these  cavities  con 
tain  smaller  cavities  of  the  same  kind  and  form,  particu- 
larly in  their  sides.  The  mountainous  ridges  which  sur- 
round, these  cavities,  reflect  the  greatest  quantity  of 
light ;  and  hence  that  region  of  the  moon  in  which  they 
abound,  appears  brighter  than  any  other.  From  their 
lying  in  every  possible  direction,  they  appear  at  and 
near  the  time  of  full  moon,  like  a  number  of  brilliant 
streaks  or  radiations.  These  radiations  appear  to  con- 
verge towards  a  large  brilliant  spot,  surrounded  by  a 
faint  shade,  near  the  lower  part  of  the  moon  which  is 
named  Tycho,  (Frontispiece,  1,)  which  may  be  easily  dis- 
tinguished even  by  a  small  telescope.  The  spots  named 
Kepler  and  Copernicus,  are  each  composed  of  a  central 
spot  with  luminous  radiations.* 

146.  Dr.  Herschel  is  supposed  also  to  have  obtained 
decisive  evidence  of  the  existence  of  volcanoes  in  the 
moon,  not  only  from  the  light  afforded  by  their  fires, 
but  also  from  the  formation  of  new  mountains  by  the 
accumulation  of  matter  where  fires  had  been  seen  to 
exist,  and  which  remained  after  the  fires  were  extinct. 

147.  Some  indications  of  an  atmosphere  about  the 
moon  have  been  obtained,  the  most  decisive  of  which 
are  derived  from  appearances  of  twilight,  a  phenomenon 
that  implies  the  presence  of  an  atmosphere.    Similar  in- 
dications have  been  detected,  it  is  supposed,  in  eclipses 
of  the  sun,  denoting  a  transparent  refracting  medium 
encompassing  the  moon. 


146.  Volcanoes. — What  proofs  are  there  of  their  having  ex- 
isted in  the  moon  ? 

147.  What  evidence  is  there  of  a  lunar  atmosphere  ? 


*  The  foregoing  accurate  description  of  the  lunar  mountains  and  car 
erns  is  from  "  Dick's  Celestial  Scenery." 


LUNAR  GEOGRAPHY.  117 

148.  It  has  been  a  question  with  astronomers,  whether 
there  is  water  in  the  moon  ?     The  general  opinion  is 
that  there  is  none.     If  there  were  any,  we   should  ex- 
pect to  see  clouds ;  or  at  least  we  should  expect  to  find 
the  face  of  the  moon  occasionally  obscured  by  clouds ; 
but  this  is*  not  the  case,  since  the  spots  on  the  moon's 
disk,  when  our  sky  is  clear,  are  always  in  full  view. 
The  deep  caverns,*  moreover,  seen  in  those  dusky  spots 
which  were  supposed  to  be  seas,  are  unfavorable  to  the 
supposition,  that  they  are  surrounded  by  water  ;  and  the 
terminator  when  it  passes  over  these  places  is,  as  already 
remarked,  too  uneven  to  permit  us  to  suppose  that  these 
tracts  are  seas. 

149.  The  improbability  of  our  ever  identifying  arti- 
ficial structures  in  the  moon,  may  be  inferred  from  the 
fact  that  a  line  one  mile  in  length  in  the  moon  subtends 
an  angle  at  the  eye  of  only  about  one  second.     If,  there- 
fore, works  of  art  were  to  have  a  sufficient  horizontal 
extent  to  become  visible,  they  can  hardly  be  supposed 
to  attain  the  necessary  elevation,  when  we  reflect  that 
the  height  of  the  great  pyramid  of  Egypt  is  less  than 
the  sixth  part  of  a  mile.     Still  less  probable  is  it  that  we 
shall  ever  discover  any  inhabitants  in  the   moon.     The 
greatest  magnifying  power  that  has  ever  been  applied 
with  distinctness,  to  the  moon,  does  not  much  exceed  a 
thousand  times,  bringing  the  moon  apparently  a  thou- 
sand times  nearer  to  us  than  when  seen  by  the  naked 
eye.     But  this  implies  a  distance  still  of  240  miles ;  and 


148.  Is  there  water  in  the  moon  ?     What  proofs  are  there 
to  the  contrary  ? 

149.  Is  it  probable  that  artificial  structures  in  the  moon  will 
ever  be  identified  ?     How  high  must  they  be,  in   order  to  be 
seen  distinct,  from  the  surface  ?     Is  it  probable  that  we  shall 
ever  be  able  to  recognize  inhabitants  in  the  moon  ?      What  is 
the  greatest  magnifying  power  of  the  telescope  that  has  ever 
been  applied  to  the  moon  ?     If  we   could  magnify  the  moon 
1 0,000  times  what  would  still  be  her  apparent  distance  ?    What 
inherent  difficulty  is  there  in  employing  very  great  magnifiers  ? 


118  THE    MOON. 

could  we  magnify  the  moon  ten  thousand  times,  her  ap- 
parent distance  would  still  be  twenty-four  miles,  a  dis- 
tance too  great  to  distinguish  living  beings.  Moreover, 
when  we  use  such  high  magnifiers  in  the  telescope,  our 
field  of  view  is  necessarily  exceedingly  small,  so  that  k 
would  be  a  mere  point  that  we  could  view  at  a  timt . 
This  difficulty  is  inherent  in  the  very  nature  of  tele> 
scopes,  namely,  that  the  field  of  view  is  reduced  as  the 
magnifying  power  is  increased  ;  and  we  magnify  the 
vapors  and  the  undulations  of  the  atmosphere,  as  well 
as  the  moon,  and  by  this  .means  impair  the  medium  so 
much  that  we  should  not  be  able  to  see  anything  with 
distinctness.  It  is  only  to  such  minute  objects  as  a  star, 
that  very  high  powers  of  the  telescope  can  ever  be  ap- 
plied. 

150.  Some  writers,  however,  suppose  that  possibly 
we  may  trace  indications  of  lunar  inhabitants  in  their 
works,  and  that  they  may,  in  like  manner,  recognize  the 
existence  of  the  inhabitants  of  our  planet.  An  author 
who  has  reflected  much  on  subjects  of  this  kind,  rea- 
sons as  follows  :  A  navigator  who  approaches  within  a 
certain  distance  of  a  small  island,  although  he  perceives 
no  Human  being  upon  it,  can  judge  with  certainty,  that 
it  is  inhabited,  if  he  perceives  human  habitations,  villa- 
ges, cornfields,  or  other  traces  of  cultivation.  In  like 
manner,  if  we  could  perceive  changes  or  operations  in 
the  moon,  which  could  be  traced  to  the  agency  of  intel- 
ligent beings,  we  should  then  obtain  satisfactory  evi- 
dence, that  such  beings  exist  on  that  planet ;  and  it  is 
thought  possible  that  such  operations  may  be  traced. 
A  telescope  which  magnifies  1200  times,  will  enable  us 
to  perceive,  as  a  visible  point  on  the  surface  of  the  moon, 
an  object  whose  diameter  is  only  about  300  feet.  Such 


150.  What  have  some  writers  supposed  with  respect  to  the 
probability  of  our  tracing  marks  of  living  beings  on  the  moon  ? 
How  is  it  proposed  to  have  the  moon  examined  for  this  pur- 
pose ? 


LUNAR  GEOGRAPHY.  119 

an  object  is  not  larger  than  many  of  our  public  edifices ; 
and,  therefore,  were  any  such  edifices  rearing  in  the 
moon,  or  were  a  town  or  city  extending  its  boundaries, 
or  were  operations  of  this  description  carrying  on  in  a 
district  where  no  such  edifices  had  previously  been 
erected,  such  objects  and  operations  might  probably  be 
detected  by  a  minute  inspection.  Were  a  multitude  of 
living  creatures  moving  from  place  to  place  in  a  body, 
or  were  they  even  encamping  in  an  extensive  plain,  like 
a  large  army,  or  like  a  tribe  of  Arabs  in  the  desert,  and 
afterwards  removing,  it  is  possible  that  such  changes 
might  be  traced  by  the  difference  of  shade  or  color, 
which  such  movements  would  produce.  In  order  to  de- 
tect such  minute  objects  and  operations,  it  would  be 
requisite  that  the  surface  of  the  moon  should  be  distrib- 
uted among  at  least  a  hundred  astronomers,  each  having 
a  spot  or  two  allotted  to  him,  as  the  object  of  his  mere 
particular  investigation,  and  that  the  observations  be 
continued  for  a  period  of  at  least  thirty  or  forty  years, 
during  which  time  certain  changes  would  probably  be 
perceived,  arising  either  from  physical  causes,  or  from 
the  operations  of  living  agents.* 

151.  It  has  sometimes  been  a  subject  of  speculation, 
whether  it  might  be  possible,  by  any  symbols,  to  cor- 
respond with  the  inhabitants  of  the  moon.  It  has  been 
suggested,  that  if  some  vast  geometrical  figure,  as  a 
square  or  a  triangle,  were  erected  on  the  plains  of  Siberia, 
it  might  be  recognized  by  the  lunarians,  and  answered 
by  some  corresponding  signal.  Some  geometrical  figure 
would  be  peculiarly  appropriate  for  such  a  telegraphic 
commerce  with  the  inhabitants  of  another  sphere,  since 
these  are  simple  ideas  common  to  all  minds. 


151 .  How  is  it  proposed  to  carry  on  a  telegraphic  communi- 
cation with  the  lunarians  ? 


»  Dick's  Celestial  Scenery,  Ch.  iv. 


r20  THE  MOON. 

PHASES  OF  THE  MOON. 

152.  The  changes  of  the  moon,  commonly  called  her 
Phases,  arise  from  different  portions  of  her  illuminated 
side  being  turned  towards  the  earth  at  different  times 
When  the  moon  is  first  seen  after  the  setting  sun,  hei 
form  is  thlt  of  a  bright  crescent,  on  the  side  of  the  disk 
next  to  the  sun,  while  the  other  portions  of  the  disk 
shine  with  a  feeble  light,  reflected  to  the  moon  from  the 
earth.  Every  night  we  observe  the  moon  to  be  farther 
and  farther  eastward  of  the  sun,  and  at  the  same  time 
the  crescent  enlarges,  until,  when  the  moon  has  reached 
an  elongation  from  the  sun  of  90°,  half  her  visible  disk 
is  enlightened,  and  she  is  said  to  be  in  her  first  quarter. 
The  terminator,  or  line  which  separates  the  illuminated 
from  the  dark  part  of  the  moon,  is  convex  towards  the 
sun  from  the  new  moon  to  the  first  quarter,  and  the 
moon  is  said  to  be  horned.  The  extremities  of  the 
crescent  are  called  cusps.  At  the  first  quarter,  the  ter- 
minator becomes  a  straight  line,  coinciding  with  a  di- 
ameter of  the  disk  ;  but  after  passing  this  point,  the  ter- 
minator becomes  concave  towards  the  sun,  bounding 
that  side  of  the  moon  by  an  elliptical  curve,  when  the 
moon  is  said  to  be  gibbous.  When  the  moon  arrives  at 
the  distance  of  180°  from  the  sun,  the  entire  circle  is 
illuminated,  and  the  moon  is  full.  She  is  then  in  oppo- 
sition to  the  sun,  rising  about  the  time  the  sun  sets.  For 
a  week  after  the  full,  the  moon  appears  gibbous  again, 
until,  having  arrived  within  90°  of  the  sun,  she  re- 
sumes the  same  form  as  at  the  first  quarter,  being  then 
at  her  third  quarter.  From  this  time  until  new  moon, 
she  exhibits  again  the  form  of  a  crescent  before  the  ri- 
sing sun,  until,  approaching  her  conjunction  with  the 


152.  Phases  of  the  Moon. — Whence  do  they  rise  ?  State 
the  successive  appearances  of  the  moon  from  new  to  full.  In 
what  parts  of  her  revolution  is  she  horned,  and  in  what  parts 
gibbous  ?  When  is  she  said  to  be  in  conjunction,  and  when  in 
opposition  ?  What  are  the  syzigies,  quadratures,  and  octants  ? 
Define  the  circle  of  illumination,  and  the  ciicle  of  the  disk. 


PHASES.       . 


121 


sun,  her  narrow  thread  of  light  is  lost  in  the  solar  blaze  ; 
and  finally,  at  the  moment  of  passing  the  sun,  the  dark 
side  is  wholly  turned  towards  us,  and  for  some  time  we 
lose  sight  of  the  moon. 

The  two  points  in  the  orbit  corresponding  to  new  and 
full  moon  respectively,  are  called  by  the  common  name 
of  syzigies ;  those  which  are  90°  from  the  sun  are 
called  quadratures ;  and  the  points  half  way  between 
the  syzigies  and  quadratures  are  called  octants.  The 
circle  which  divides  the  enlightened  from  the  unen- 
lightened hemisphere  of  the  moon,  is  called  the  circle  of 
illumination:  that  which  divides  the  hemisphere  that 
is  turned-  towards  us  from  the  hemisphere  that  is  turn- 
ed from  us,  is  called  the  circle  of  the  disk. 

153.  As  the  moon  is  an  opake  body  of  a  spherical 
figure,  and  borrows  her  light  from  the  sun,  it  is  obvious 

Fig.  31 


that  that  half  only  which  is  towards  the  sun  can  be  il- 
luminated.' More  or  less  of  this  side  is  turned  towards 
the  earth,  according  as  the  moon  is  at  a  greater  or  less 
elongation  from  the  sun.  The  reason  of  the  different 
phases  will  be  best  understood  from  a  diagram.  There- 
fore let  T  (Fig.  31,)  represent  the  earth,  and  S  the  sun. 

11 


122  THE  MOON. 

Let  A,  B,  C,  <fec.  be  successive  positions  of  the  moon. 
At  A  the  entire  dark  side  of  the  moon  being  turned  to- 
wards the  earth,  the  disk  would  be  wholly  invisible.  Al 
B,  the  circle  of  the  disk  cuts  of  a  small  part  of  the  en 
lightened  hemisphere,  which  appears  in  the  heavens  at 
b,  under  the  form  of  a  crescent.  At  C,  the  first  quarter 
the  circle  of  the  disk  cuts  off  half  the  enlightened  hem- 
isphere, and  a  half  moon  is  seen  at  c.  In  like  manner  it 
will  be  seen  that  the  appearances  presented  at  D,  E,  F, 
&c.  must  be  those  represented  at  d,  e,f.  If  a  round 
body,  as  an  apple,  suspended  by  a  string,  be  carried 
around  a  lamp,  the  eye  remaining  fixed  opposite  to  it  at 
the  same  level,  the  various  phases  of  the  moon  will  be 
exhibited. 

REVOLUTIONS  OF  THE  MOON. 

1 54.  The  moon  revolves  around  the  earth  from  west 
to  east,  making  the  entire  circuit  of  the  heavens  in  about 
271  days. 

The  period  of  the  moon's  revolution  from  any  point 
in  the  heavens  round  to  the  same  point  again,  is  called 
a  month.  A  sidereal  month  is  the  time  of  the  moon's 
passing  from  any  star,  until  it  returns  to  the  same  star 
again.  A  synodical  month,  so  called  from  two  Greek 
words  implying  that  at  the  end  of  this  period  the  two 
bodies  (the  sun  and  moon)  come  together,  is  the  time 
from  one  conjunction  or  new  moon  to  another.  The 
synodical  month  is  about  29J  days,  or  more  exactly, 
29d.  12h.  44m.  2s.S=  29.53  days.  The  sidereal  month 
is  about  two  days  shorter,  being  27d.  7h.  43m.  lls.5. 
or  27.32  days.  As  the  sun  and  moon  are  both  revolv- 
ing in  the  same  direction,  and  the  sun  is  moving  nearly 


153.  How  much  of  the  moon  is  illuminated  at  once?     Ex- 
plain the  phases  of  the  moon  from  figure  31. 

1 54.  Define  a  month.     Define  a  sidereal  month.     Also  a  sy- 
nodical month.     Why  so  called  ?     What  is  the  length  of  the 
Bynodical  month  ?     Also  of  the  sidereal  month  ?     What  is  the 
moon's  daily  motion  ? 


„       REVOLUTIONS.  123 

a  degree  a  day,  during  the  27  days  of  the  moan's  revo- 
lution, the  sun  must  have  moved  27°.  Now  since  the 
moon  passes  over  360°  in  27.32  days,  her  daily  motion 
must  be  13°  17'.  It  must  therefore  evidently  take  about 
two  days  for  the  moon  to  overtake  the  sun. 

155.  The  moon's  orbit  is  inclined  to  the  ecliptic  in  an 
angle  of  about  5°  (5°   8'  48".)     The  moon  crosses  the 
ecliptic  in  two  opposite  points  called  her  nodes.     That 
which  the  moon  crosses  from  south  to  north,  is  called 
her  ascending  node,  that  which  she  crosses  from  north 
to  south,  her  descending  node.     The  moon,  therefore,  is 
never  seen  far  from  the  ecliptic,  but  the  path  she  pur- 
sues through  the  skies,  is  very  nearly  the  same  as  that 
of  (the  sun  in  his  annular  revolution  around  the  earth. 

156.  The  moon,  at  the  same  age,  crosses  the  meridian 
at  different  altitudes  at  different  seasons  of  the  year ;  and 
accordingly  it  is  said  to  run  sometimes  high  and  some- 
times low.     The  full  moon,  for  example,  will  appear 
much  farther  in  tne  south  when  on  the  meridian  at  one 
period  of  the  year  than  at  another.     The  reason  of  this 
may  be  explained  as  follows.     When  the  sun  is  in  the 
part  of  the  ecliptic  south  of  the  equator,  the  earth  and 
of  course  the  moon,  which  always  keeps  near  to  the 
earth,  is  in  the  part  north  of  the  equator.     At  such 
times,  therefore,  the  new  moons,   which   are    always 
seen  in  the  part  of  the  heavens  where  the  sun  is,  will 
run  far  south,  while  the  full  moons,  which  are  always  in 
the  opposite  part  of  the  heavens  from  the  sun,  will  run 
high.     Such  is  the  case  during  the  winter  months  ;  but, 


J  55.  How  much  is  the  moon's  orbit  inclined  to  the  ecliptic  ? 
Define  the  nodes.  What  is  the  ascending  and  what  the  de- 
scending node  ? 

1 56.  Why  does  the  moon  run  high  and  low  ?  At  what  sea- 
son of  the  year  are  the  full  moons  longest  above  the  horizon  ? 
Explain  how  this  operates  favorably  to  those  who  are  near 
the  pole. 


124  THE  MOON. 

in  the  summer,  when  the  sun  is  towards  the  northern 
tropic  and  the  earth  towards  the  southern,  the  new 
moons  run  high  and  the  full  moons  low.  This  arrange- 
ment gives  us  a  great  advantage  in  respect  to  the  amount 
of  light  received  from  the  moon ;  since  the  full  moon 
is  longest  above  the  horizon  during  the  long  nights  of 
winter,  when  her  presence  is  most  needed,  This  cir- 
cumstance is  especially  favorable  to  the  inhabitants  of 
the  polar  regions,  the  moon,  when  full,  traversing  that 
part  of  her  orbit  which  lies  north  of  the  equator,  and  of 
course  above  the  horizon  of  the  north  pole,  and  traver- 
sing the  portion  that  lies  south  of  the  equator,  and  be- 
low the  polar  horizon,  when  new.  During  the  polar 
winter,  therefore,  the  moon,  during  her  second  and  third 
quarters,  when  she  gives  most  light,  is  commonly  above 
the  horizon,  while  the  sun  is  absent ;  w^hereas,  during 
summer,  while  the  sun  is  present  and  the  light  is  not 
needed,  during  her  second  and  third  quarters,  she  is  be- 
low the  horizon. 

157.  About  the  time  of  the  autumnal  equinox,  the 
moon  when  near  the  full,  rises  about  sunset  Tor  a  num- 
ber of  nights  in  succession ;  and  as  this  is,  in  England, 
the  period  of  harvest,'  the  phenomenon  is  called  the 
Harvest  Moon.  To  understand  the  reason  of  this,  since 
the  moon  is  never  far  from  the  ecliptic,  we  will  suppose 
her  progress  to  be  in  the  ecliptic.  If  the  moon  moved 
in  the  equator,  then,  since  this  great  circle  is  at  right 
angles  to  the  axis  of  the  earth,  all  parts  of  it,  as  the 
earth  revolves,  cut  the  horizon  at  the  same  constant 
angle.  But  the  moon's  orbit,  or  the  ecliptic,  which  is 
here  taken  to  represent  it,  being  oblique  to  the  equator, 
cuts  the 'horizon  at  different  angles  in  different  parts,  as 
will  easily  be  seen  by  reference  to  an  artificial  globe. 
When  the  first  of  Aries,  or  vernal  equinox,  is  in  the 


157.  Why  is  the  harvest  moon  so  called  ?  Explain  its  cause. 
How  is  the  moon's  orbit  inclined  to  the  horizon  at  different 


times  ? 


REVOLUTIONS.  125 

eastern  horizon,  it  will  be  seen  that  the  ecliptic,  (and 
consequently  the  moon's  orbit,)  makes  its  least  angle 
with  the  horizon.  Now,  at  the  autumnal  equinox,  the 
sun  being  in  Libra,  the  moon  at  the  full,  when  she  is 
always  opposite  to  the  sun,  is  in  Aries,  and  rises  when 
the  sun  sets.  On  the  following  evening,  although  she 
has  advanced  in  her  orbit  about  13°,  yet  her  progress  be- 
ing oblique  to  the  horizon,  and  at  a  small  angle  with  it, 
she  will  be  found  at  this  time  but  a  little  way  below  the 
horizon,  compared  with  the  point  where  she  was  at  sun- 
set the  preceding  evening.  She  therefore  rises  but  little 
later,  and  so  for  a  week  only  a  little  later  each  evening 
than  she  did  the  preceding  night. 

1 58.  The  moon  turns  on  its  axis  in  the  same  time  in 
which  it  revolves  around  the  earth. 

This  is  known  by  the  moon's  always  keeping  nearly 
the  'same  face  towards  us,  as  is  indicated  by  the  tele 
scope,  which  could  not  happen  unless  her  revolution  on 
her  axis  kept  pace  with  her  motion  in  her  orbit.  Thus 
it  will  be  seen  by  inspecting  figure  22,  that  the  earth 
turns  different  faces  towards  the  sun  at  different  times  ; 
and  if  a  ball  having  one  hemisphere  white  and  the 
other  black  be  carried  around  a  lamp,  it  will  easily  be 
seen  that  it  cannot  present  the  same  face  constantly  to- 
wards the  lamp  unless  it  turns  once  on  its  axis  while 
performing  its  revolution.  The  same  thing  will  be  ob- 
served when  a  man  walks  around  a  tree,  keeping  his  face 
constantly  towards  it.  Since  however  the  motion  ot 
the  moon  on  its  axis  is  uniform,  while  the  motion  in  its 
orbit  is  unequal,  the  moon  does  in  fact  reveal  to  us  a  lit- 
tle sometimes  of  one  side  and  sometimes  of  the  other. 
Thus  when  the  ball  above  mentioned  is  placed  before 
the  eye  wi^h  its  light  side  towards  us,  on  carrying  it 
round,  if  it  is  moved  faster  than  it  is  turned  on  its  axis, 


1 58.  In  what  time  does  the  moon  turn  on  its  axis  ?  Illus- 
trate by  the  motion  of  a  ball  around  a  lamp.  Is  the  same  side 
of  the  moop  always  turned  exactly  towards  us  ? 

U* 


126  THE    MOON. 

a  portion  of  the  dark  hemisphere  is  brought  into  view 
on  one  side  ;  or  if  it  is  moved  forward  slower  than  it  is 
turned  on  its  axis,  a  portion  of  the  dark  hemisphere 
comes  into  view  on  the  other  side. 

159.  These  appearances  are  called  the  moon's  libra- 
tions  in  longitude.  The  moon  has  also  a  libration  in 
latitude,  so  called,  because  in  one  part  of  her  revolution, 
more  of  the  region  around  one  of  the  poles  comes  into 
view,  and  in  another  part  of  the  revolution,  more  of  the 
region  around  the  other  pole  ;  which  gives  the  appear- 
ance of  a  tilting  motion  to  the  moon's  axis.  This  has 
nearly  the  same  cause  with  that  which  occasions  our 
change  of  seasons.  The  moon's  axis  being  inclined  to 
the  plane  of  her  orbit,  and  always  remaining  parallel  to 
itself,  the  circle  which  divides  the  visible  from  the  in- 
visible part  of  the  moon,  will  pass  in  such  a  way  as  to 
throw  sometimes  more  of  one  pole  into  view,  and  some- 
times more  of  the  other,  as  would  be  the  case  with  the 
earth  if  seen  from  the  sun.  (See  Fig.  22.) 

The  moon  exhibits  another  phenomenon  of  this  kind 
called  her  diurnal  libration,  depending  on  the  daily  ro- 
tation of  the  spectator.  She  turns  the  same  face  to- 
wards the  center  of  the  earth  only,  whereas  we  view 
her  from  the  surface.  When  she  is  on  the  meridian,  we 
see  her  disk  nearly  as  though  we  viewed  it  from  the 
center  of  the  earth,  and  hence  in  this  situation  it  is  sub- 
ject to  little  change ;  but  when  near  the  horizon,  our 
circle  of  vision  takes  in  more  of  the  upper  limb  than 
would  be  presented  to  a  spectator  at  the  center  of  the 
earth.  Hence,  from  this  cause,  we  see  a  portion  of  one 
limb  while  the  moon  is  rising,  which  is  gradually  lost 
sight  of,  and  we  see  a  portion  of  the  opposite  limb  as 
the  moon  declines  to  the  west.  It  will  be  remarked 
that  neither  of  the  foregoing  changes  implies  any  actual 
motion  in  the  moon,  but  that  each  arises  from  a  change 
of  position  in  the  spectator. 


159.  Explain  lie  librations  in  longitude.     Ditto  in  latitude 
Ditto  the  diurnal  librations. 


REVOLUTIONS. 


160.  Since  the  succession  of  day  and  night  depends 
on  the  revolution  of  a  planet  on  its  own  axis,  an  inhab- 
itant of  the  moon  would  have  but  one  day  and  one  night 
during  the  whole  lunar  month  of  29J  days.  One  of  its 
days,  therefore,  is  equal  to  nearly  15  of  ours.  So  pro- 
tracted an  exposure  to  the  sun's  rays,  especially  in  the 
equatorial  regions  of  the  moon,  must  occasion  an  exces- 
sive accumulation  of  heat  ;  and  so  long  an  absence  of 
the  sun  must  occasion  a  corresponding  degree  of  cold. 
Each  day  would  be  a  wearisome  summer  ;  each  night  a 
severe  winter.*  A  spectator  on  the  side  of  the  moon 
which  is  opposite  to  us  would  never  see  the  earth  ;  but 
one  on  the  side  next  to  us  would  see  the  earth  present- 
ing a  gradual  succession'  of  changes  during  his  long 
night  of  360  hours.  Soon  after  the  earth's  conjunction 
with  the  sun,  he  would  have  the  light  of  the  earth  re- 
flected to  him,  presenting  at  first  a  crescent,  but  enlarg- 
ing as  the  earth  approaches  its  opposition,  to  a  great  orb, 
13  times  as  large  as  the  full  moon  appears  to  us,  and  af- 
fording nearly  13  times  as  much  light.  Our  seas,  our 
plains,  our  mountains,  our  volcanoes,  and  our  clouds, 
would  produce  very  diversified  appearances,  as  would 
the  various  parts  of  the  earth  brought  successively  into 
view  by  its  diurnal  rotation.  The  earth  while  in  view 
to  an  inhabitant  of  the  moon,  would  remain  immovably 
•fixed  in  the  same  part  of  the  heavens.  For  being  un- 
conscious of  his  own  motion  around  the  earth,  as  we  are 
of  our  motion  around  the  sun,  the  earth  would  seem  to 
revolve  around  his  own  planet  from  west  to  east,  just  as 
the  moon  appears  to  us  to  revolve  about  the  earth  ;  but, 
meanwhile,  his  rotation  along  with  the  moon  on  her 
axis,  would  cause  the  earth  to  have  an  apparent  motion 


160.  How  many  days  would  an  inhabitant  of  the  moon  have 
in  a  lunar  month  ?  What  vicissitudes  of  temperature  would 
occur  in  a  single  day  ?  Would  a  spectator  on  the  side  of  the 
moon  opposite  to  us,  ever  see  the  earth  1  How  would  the  earth 
appear  to  a  spectator  on  the  side  of  the  moon  next  to  us  ? 

*  Francceur,  Uranog.  p.  91. 


128  THE  MOON. 

westward  at  the  same  rate.  The  two  motions,  there- 
fore, would  exactly  balance  each  other,  and  the  earth 
would  appear  all  the  while -at  rest. 

161.  We  have  thus  far  contemplated  the  revolution 
of  the  moon  around  the  earth  as  though  the  earth  were 
at  rest.  But,  in  order  to  have  just  ideas  respecting  the 
moon's  motions,  we  must  recollect  that  the  moon  like- 
wise revolves  along  with  the  earth  around  the  sun.  It 
is  sometimes  said  that  the  earth  carries  the  moon  along 
with  her  in  her  annual  revolution.  This  language  may 
convey  an  erroneous  idea ;  for  the  moon,  as  well  as  the 
earth,  revolves  around  the  sun  under  the  influence  of 
two  forces,  and  would  continue  her  motion  around  the 
sun  were  the  earth  removed  out  of  the  way.  Indeed, 
the  moon  is  attracted  towards  the  sun  2J  times  more 
than  towards  the  earth,  and  would  abandon  the  earth 
were  not  the  latter  also  carried  along  with  her  by  the 
same  forces.  So  far  as  the  sun  acts  equally  on  both 
bodies,  their  motion  with  respect  to  each  other  would 
not  be  disturbed.  Because  the  gravity  of  the  moon  to- 
wards the  sun  is  found  to  be  greater,  at  the*conjunction, 
than  her  gravity  towards  the  earth,  some  have  appre- 
hended that,  if  the  doctrine  of  universal  gravitation  is 
true,  the  moon  ought  necessarily  to  abandon  the  earth. 
In  order  to  understand  the  reason  why  it  does  not  do 
thus,  we  must  reflect,  that  when  a  body  is  revolving  in 
its  orbit  under  the  action  of  the  projectile  force  and 
gravity,  whatever  diminishes  the  force  of  gravity  while 
that  of  projection  remains  the  same,  causes  the  body  to 
approach  nearer  to  the  tangent  of  her  orbit,  and  of  course 
to  recede  from  the  center ;  and  whatever  increases  the 
amount  of  gravity  carries  the  body  towards  the  center. 


161.  Can  it  be  said  that  the  earth  carries  the  moon  around 
the  sun  ?  How  much  more  is  the  moon  attracted  towards  tho 
sun  than  towards  the  earth  ?  Why  does  not  the  moon  abandon 
the  earth  ?  When  the  sun  acts  equally  on  both  bodies,  does  it 
disturb  their  relative  places  ?  How  does  the  sun  act  upon 
these  bodies  at  the  conjunctions  and  oppositions  ? 


REVOLUTIONS.  129 

Now,  when  the  moon  is  in  conjunction,  her  gravity  to- 
wards the  earth  acts  in  opposition  to  that  towards  the 
sun,  while  her  velocity  remains  too  great  to  carry  her, 
with  what  force  remains,  in  a  circle  about  the  sun,  and 
she  therefore  recedes  from  the  sun,  and  commences  her 
revolution  around  the  earth.  On  arriving  at  the  opposi- 
tion, the  gravity  of  the  earth  conspires  with  that  of  the 
sun,  and  the  moon's  projectile  force  being  less  than  that 
required  to  make  her  revolve  in  a  circular  orbit,  when 
attracted  towards  the  sun  by  the  sum  of  these  forces,  she 
accordingly  begins  to  approach  the  sun  and  descends 
again  to  the  conjunction. 

162.  The  attraction  of  the  sun,  however,  being  every 
where  greater  than  that  of  the  earth,  the  actual  path  of 
the  moon  around  the  sun  is  every  where  concave  to- 
wards the  latter.  Still  the  elliptical  path  of  the  moon 
around  the  earth,  is  to  be  conceived  of  in  the  same  way 
as  though  both  bodies  were  at  rest  with  respect  to  the 
sun.  Thus,  while  a  steamboat  is  passing  swiftly  around 
an  island,  and  a  man  is  walking  slowly  around  a  post  in 
the  cabin,  the  line  which  he  describes  in  space  between 
the  forward  motion  of  the  boat  and  his  circular  motion 
around  the  post,  may  be  every  where  concave  towards 
the  island,  while  his  path  around  the  post  will  still  be 
the  same  as  though  both  were  at  rest.  A  nail  in  the  rim 
of  a  coach  wheel,  will  turn  around  the  axis  of  the  wheel, 
when  the  coach  has  a  forward  motion  in  the  same  man- 
ner as  when  the  coach  is  at  rest,  although  the  line  ac- 
tually described  by  the  nail  will  be  the  resultant  of  both 
motions,  and  very  different  from  either. 

168.  We  have  hitherto  regarded  the  moon  as  descri- 
bing a  great  circle  on  the  face  of  the  sky,  such  being  the 


162.  How  is  the  moon's  path  in  space  with  respect  to  the 
sun  1  How  is  the  elliptical  path  of  the  moon  around  the  earth 
to  be  conceived  of  ?  How  is  this  illustrated  by  the  motions  of 
a  man  in  a  steamboat  ?  Alsc  by  the  motions  of  a  nail  in  die 
rim  of  a  coach  wheel  ? 


130  THE  MOON. 

visible  orbit  as  seen  by  projection.  But,  on  more  exact 
investigation,  it  is  found  that  her  orbit  is  not  a  circle, 
and  that  her  motions  are  subject  to  very  numerous  ir- 
regularities. These  will  be  best  understood  in  connec- 
tion with  the  causes  on  which  they  depend.  The  law 
of  universal  gravitation  has  been  applied  with  wonder- 
ful success  to  their  investigation,  and  its  results  have 
conspired  with  those  of  long  continued  observation,  to 
furnish  the  means  of  ascertaining  with  great  exactness 
the  place  of  the  moon  in  the  heavens  at  any  given  in- 
stant of  time,  past  or  future,  and  thus  to  enable  astrono- 
mers to  determine  longitudes,  to  calculate  eclipses,  and 
to  solve  various  other  problems  of  the  highest  interest. 
A  complete  understanding  of  all  the  irregularities  of  the 
moon's  motions,  must  be  sought  for  in  more  extensive 
treatises  of  astronomy  than  the  present ;  but  some  gen- 
eral acquaintance  with  the  subject,  clear  and  intelligible 
as  far  as  it  goes,  may  be  acquired  by  first  gaining  a  dis- 
tinct idea  of  the  mutual  actions  of  the  sun,  the  moon, 
and  the  earth. 

164.  The  irregularities  of  the  moon's  motions,  are 
due  chiefly  to  the  disturbing  influence  of  the  sun,  which 
operates  in  two  ways ;  first,  by  acting  unequally  on  the 
earth  and  moon,  and,  secondly,  by  acting  obliquely  on 
the  moon,  on  account  of  the  inclination  of  her  orbit  to 
the  ecliptic. 

If  the  sun  acted  equally  on  the  earth  and  moon,  and 
always  in  parallel  lines,  this  action  would  serve  only  to 
restrain  them  in  their  annual  motions  round  the  sun,  and 
would  not  affect  their  actions  on  each  other,  or  their 
motions  about  their  common  center  of  gravity.  In  that 
case,  if  they  were  allowed  to  fall  directly  towards  the 
sun,  they  would  fall  equally,  and  their  respective  situa- 
tions would  not  be  affected  by  their  descending  equally 
towards  it.  We  might  then  conceive  them  as  in  a 
plane,  every  part  of  which  being  equally  acted  on  by 


163.  Are  the  motions  of  the  moon  regular  or  irregular  ?     By 
what,  general  law  are  they  explained  ? 


REVOLUTIONS.  131 

the  sun,  the  whole  plane  would  descend  towards  the 
sun,  but  the  respective  motions  of  the  earth  and  the 
moon  in  this  plane,  would  be  the  same  as  if  it  were 
quiescent.  Supposing  then  this  plane  and  all  in  it, 
to  have  an  annual  motion  imprinted  on  it,  it  would 
move  regularly  around  the  sun,  while  the  earth  and  moon 
would  move  in  it  with  respect  to  each  other,  as  if  the 
plane  were  at  rest,  without  any  irregularities.  But  be- 
cause the  moon  is  nearer  the  sun  in  one  half  of  her  orbit 
than  the  earth  is,  and  in  the  other  half  of  her  orbit  is  at 
a  greater  distance  than  the  earth  from  the  sun,  while  the 
power  of  gravity  is  always  greater  at  a  less  distance  ;  it 
follows,  that  in  one  half  of  her  orbit  the  moon  is  more 
attracted  than  the  earth  towards  the  sun,  and  in  the  other 
half  less  attracted  than  the  earth.  The  excess  of  the 
attraction,  in  the  first  case,  and  the  defect  in  the  second, 
constitutes  a  disturbing  force,  to  which  we  may  add  an- 
other, namely,  that  arising  from  the  oblique  action  of  the 
solar  force,  since  this  action  is  not  directed  in  parallel 
lines,  but  in  lines  that  meet  in  the  center  of  the  sun. 

165.  To  see  the  effects  of  this  process,  let  us  suppose 
that  the  projectile  motions  of  the  earth  and  moon  were 
destroyed,  and  that  they  were  allowed  to  fall  freely  to- 
wards the  sun.  If  the  moon  was  in  conjunction  with 
the  sun,  or  in  that  part  of  her  orbit  which  is  nearest  to 
him,  the  moon  would  be  more  attracted  than  the  earth, 
and  fall  with  greater  velocity  towards  the  sun ;  so  that 
the  distance  of  the  moon  from  the  earth  would  be  in- 
creased in  the  fall.  If  the  moon  was  in  opposition,  or 


164.  To  what  cause  are  the  inequalities  of  the  moons  mo- 
tions chiefly  due  ?     If  the  sun  acted  equally  on  the  earth  and 
moon,  and  in  parallel  lines,  would  it  disturb  their  motions  ?     If 
allowed  to  fall  towards  the  sun,  how  would  they  fall  ?     How 
might  we  conceive  them  as  situated  in  a  plane  ?     When  is  the 
moon  more  attracted  than  the  earth  ?      When  is  the.earth  more 
attracted  than  the  moon  ?   What  constitutes  the  disturbing  face. 

165.  Trace  the  effects  of  the  sun,  if  the  projectile  force  were 
destroved,  at  conjunction,  at  opposition,  and  at  quadrature. 


132  'THE  MOON. 


in  the  part  of  her  orbit  which  is  farthest  from  the  sun, 
she  would  be  less  attracted  than  the  earth  by  the  sun, 
and  would  fall  with  a  less  velocity  towards  the  sun,  and 
would  be  left  behind  ;  so  that  the  distance  of  the  moon 
from  the  earth  would  be  increased  in  this  case  also.  If 
the  moon  was  in  one  of  the  quarters,  then  the  earth  and 
moon  being  both  attracted  towards  the  center  of  the 
sun,  they  would  both  descend  directly  towards  that  cen- 
ter, and  by  approaching  it,  they  would  necessarily  at 
the  same  time  approach  each  other,  and  in  this  case  their 
distance  from  each  other  would  be  diminished.  Now 
whenever  the  action  of  the  sun  would  increase  their  dis- 
tance, if  they  were  allowed  to  fall  towards  the  sun, 
then  the  sun's  action,  by  endeavouring  to  separate  them 
diminishes  their  gravity  to  each  other;  whenever  the 
sun's  action  would  diminish  the  distance,  then  it  in- 
creases their  mutual  gravitation.  Hence,  in  the  con 
junction  and  opposition,  that  is,  in  the  syzigies,  their 
gravity  towards  each  other  is  diminished  by  the  action 
of  the  sun,  while  in  the  quadratures  it  is  increased. 
But  it  must  be  remembered  that  it  is  not  the  total  action 
of  the  sun  on  them  that  disturbs  their  motions,  but  only 
that  part  of  it  which  tends  at  one  time  to  separate  them, 
and  at  another  time  to  bring  them  nearer  together.  The 
other  and  far  greater  part,  has  no  other  effect  than  to 
retain  them  in  their  annual  course  around  the  sun. 

166.  The  figure  of  the  moon's  orbit  is  an  ellipse,  hav- 
ing the  earth  in  one  of  the  foci. 

The  greatest  and  least  distances  of  the  moon  from  the 
earth,  are  nearly  64  and  56,  the  radius  of  the  earth  being 
taken  for  unity.  Hence,  taking  the  arithmetical  mean, 
we  find  that  the  mean  distance  of  the  moon  from  the 


166.  What  is  the  figure  of  the  moon's  orbit  ?  What  are  the 
greatest  and  least  distances  of  the  moon  from  the  earth  ?  De- 
fine the  terms  perigee  and  apogee.  What  numbers  express  the 
greatest  and  least  distance  of  the  sun  from  the  earth  ?  How 
does  the  eccentricity  of  the  lunar  orbit,  compare  with  that  of 
the  solar  ? 


REVOLUTIONS.  133 

earth  is  very  nearly  60  times  the  radius  of  the  earth. 
The  point  in  the  moon's  orbit  nearest  the  earth,  is 
called  her  perigee ;  the  point  farthest  from  the  earth, 
her  apogee. 

The  greatest  and  least  distances  of  the  sun  are  re- 
spectively as  the  numbers  32.583,  and  31.517.  By  com- 
paring this  ratio  with  that  of  the  distances  of  the  moon, 
it  will  be  seen  that  the  latter  vary  much  more  than  the 
former,  and  consequently  that  the  lunar  orbit  is  much 
more  eccentric  than  the  solar.  The  eccentricity  of  the 
moon's  orbit  is  in  fact  ^§  of  its  mean  distance  from  the 
earth,  while  that  of  the  earth  is  only  •£$  of  its  mean  dis- 
tance from  the  sun, 

167.  The  moon1  s  nodes  constantly  shift  their  positions 
in  the  ecliptic  from  east  to  west,  at  the  rate  of  19°  35'  per 
annum,  returning  to  the  same  points  in  18.6  years. 

Suppose  the  great  circle  of  the  ecliptic  marked  out  on 
the  face  of  the  sky  in  a  distinct  line,  and  let  us  observe, 
at  any  given  time,  the  exact  point  where  the  moon 
crosses  this  line,  which  we  will  suppose  to  be  close  to  a 
certain  star  ;  then,  on  its  next  return  to  that  part  of  the 
heavens,  we  shall  find  that  it  crosses  the  ecliptic  sensi- 
bly to  the  westward  of  that  star,  and  so  on,  farther  and 
farther  to  the  westward  every  time  it  crosses  the  ecliptic 
at  either  node.  This  fact  is  expressed  by  saying  that 
the  nodes  retrograde  on  the  ecliptic,  and  that  the  line 
which  joins  them,  or  the  line  of  the  nodes,  revolves  from 
east  to  west. 

1 68.  The  period  occupied  by  the  sun  in  passing  from 
one  of  the  moon's  nodes  until  it  comes  round  to  the 
same  node  again,  is  called  the  synodical  revolution  of  the 
node.     This  period  is  shorter  than  the  sidereal  year,  be- 
ing only  about  3461  days.     For  since  the  node  shifts  its 


167.  How  do  the  moon's  nodes  shift  their  position  ?  In 
what  time  do  they  make  a  complete  revolutin  in  the  ecliptic  ? 
Explain  what  is  mean*  by  saying  that  the  nodes  retrogade. 

12 


134  THE  MOON. 

place  to  the  westward  19°  35'  per  annum,  the  sun,  in 
his  annual  revolution,  comes  to  it  so  much  before  he 
completes  his  entire  circuit ;  and  since  the  sun  moves 
about  a  degree  a  day,  the  synodical  revolution  of  the 
node  is  365— -19=346,  or  more  exactly,  346.619851. 
The  time  from  one  new  moon,  or  from  one  full  moon, 
to  another,  is  29.5305887  days.  Now  19  synodical  rev- 
olutions of  the  nodes  contain  very  nearly  223  of  these 
periods. 

For  346.619851  x  19  =  6585.78. 
And  29.5305887x223  =  6585.32. 
Hence,  if  the  sun  and  moon  were  to  leave  the  moon's 
node  together,  after  the  sun  had  been  round  to  the  same 
node  19  times,  the  moon  would  have  made  very  nearly 
223  conjunctions  with  the  sun,  and  would  therefore,  at 
the  end  of  this  period  meet  at  the  same  node,  to  repeat 
the  same  circuit.  And  since  eclipses  of  the  sun  and 
moon  depend  upon  the  relative  position  of  the  sun,  the 
moon,  and  node,  these  phenomena  are  repeated  in  nearly 
the  same  order,  in  each  of  those  periods.  Hence,  this 
period,  consisting  of  about  18  years  and  10  days,  under 
the  name  of  the  Saros,  was  used  by  the  Chaldeans  and 
other  ancient  nations  in  predicting  eclipses. 

169.  The  Metonic  Cycle  is  not  the  same  with  the  Sa- 
ros, but  consists  of  19  tropical  years.  During  this  pe- 
riod the  moon  makes  very  nearly  235  synodical  revolu- 
tions, and  hence  the  new  and  full  moons,  if  reckoned 
by  periods  of  19  years,  recur  at  the  same  dates.  If,  for 
example,  a  new  moon  fell  on  the  fiftieth  day  of  one 
cycle,  it  would  also  fall  on  the  fiftieth  day  of  each  suc- 


168.  What  is  meant  by  the  synodical  revolution  of  the  node  ? 
How  many  new  moons  occur  in  19  synodical  revolutions  of  the 
node  ?  Why  was  this  period  used  in  predicting  eclipses  ?  What 
was  it  called  ? 

169.  What  is  the  period  of  the  Metonic  Cycle  ?     How  many 
conjunctions  of  the  moon  with  the  sun  occur  during  this  pe- 
riod ?     What  use  did  the  Athenians  make  of  this  lunar  cycle  ? 


REVOLUTIONS.  135 

ceeding  cycle ;  and,  since  the  regulation  of  games, 
feasts,  and*  fasts,  has  been  made  very  extensively  ac- 
cording to  new  or  full  moons,  hence  this  lunar  cycle  has 
been  much  used  both  in  ancient  and  modern  times. 
The  Athenians  adopted  it  433  years  before  the  Christian 
era,  for  the  regulation  of  their  calendar,  and  had  it  in- 
scribed in  letters  of  gold  on  the  walls  of  the  temple  of 
Minerva.  Hence  the  term  Golden  Number,  which  de- 
notes the  year  of  the  lunar  cycle. 

170.  The  line  of  the  apsides  of  the  moon's  orbit  re- 
volves from  west  to  east  through  her  whole  orbit  in  about 
nine  years. 

If,  in  any  revolution  of  the  moon,  we  should  accu- 
rately mark  the  place  in  the  heavens  where  the  moon 
comes  to  its  perigee,  (which  would  be  known  by  the 
moon's  apparent  diameter  being  then  greatest,)  we  should 
find,  that  at  the  next  revolution,  it  would  come  to  its 
perigee  at  a  point  a  little  farther  eastward  than  before, 
and  'so  on  at  every  revolution,  until,  after  nine  years,  it 
would  come  to  its  perigee  at  nearly  the  same  point  as  at 
first.  This  fact  is  expressed  by  saying  that  the  perigee 
and  of  course  the  apogee,  revolves,  and  that  the  line 
which  joins  these  two  points,  or  the  line  of  the  apsides, 
also  revolves. 

171.  The  inequalities  of  the  moon's  motions  are  di- 
vided into  periodical  and  secular.     Periodical  inequal- 
ities are  those  which  are  completed  in  comparatively 
short  periods.      Secular  inequalities  are  those  which 
are  completed  only  in  very  long  periods,  such  as  cen- 
turies or  ages.     Hence  the  corresponding  terms  peri- 
odical equations  and  secular  equations.     As  an  exam- 
ple of  a  secular  inequality,  we  may  mention  the  ac- 
celeration of   the   moon's  mean  motion.     It   is   discov- 
ered, that  the  moon  actually  revolves  around  the  earth 


170.  In  what  period  does  the  line  of  the  apsides  revolve? 
Explain  what  is  meant  by  this. 


136  THE    MOON. 

in  less  time  now  than  she  did  in  ancient  times.  The 
difference  however  is  exceedingly  small,  being  only 
about  10"  in  a  century,  but  increases  from  century  to 
century  as  the  square  of  the  number  of  centuries.  This 
remarkable  fact  was  discovered  by  Dr.  Halley,*  In  a 
lunar  eclipse'  the  moon's  longitude  differs  from  that  of 
the  sun,  at  the  middle  of  the  eclipse,  by  exactly  180°  ; 
and  since  the  sun's  longitude  at  any  given  time  of  the 
year  is  known,  if  we  can  learn  the  day  and  hour  when 
an  eclipse  occurs,  we  shall  of  course  know  the  longitude 
of  the  sun  and  moon.  Now  in  the  year  721  before  the 
Christian  era,  on  a  specified  day  and  hour,  Ptolemy  re- 
cords a  lunar  eclipse  to  have  happened,  and  to  have  been 
observed  by  the  Chaldeans.  The  moon's  longitude, 
therefore,  for  that  time  is  known  ;  and  as  we  know  the 
mean  motions  of  the  moon  at  present,  starting  from  that 
epoch,  and  computing,  as  may  easily  be  done,  the  place 
which  the  moon  ought  to  occupy  at  present  at  any  given 
time,  she  is  found  to  be  actually  nearly  a  degree  and  a 
half  in  advance  of  that  place.  Moreover,  the  same  con- 
clusion is  derived  from  a  comparison  of  the  Chaldean 
observations  with  those  made  by  an  Arabian  astronomer 
of  the  tenth  century. 

This  phenomenon  at  first  led  astronomers  to  appre- 
hend that  the  moon  encountered  a  resisting  medium, 
which,  by  destroying  at  every  revolution  a  small  portion 
of  her  projectile  force,  would  have  the  effect  to  bring 
her  nearer  and  nearer  to  the  earth  and  thus  to  augment 
her  velocity.  But  in  1786,  La  Place  demonstrated  that 


171 .  How  are  the  inequalities  of  the  moon's  motions  divided? 
What  are  periodical  inequalities  ?  What  are  secular  inequali- 
ties ?  Give  an  example  of  a  secular  inequality.  How  is  it 
known  that  the  moon's  motions  are  accelerated  ?  What  is  the 
amount  of  the  acceleration  per  century  ?  Will  they  a' ways 
continue  to  be  accelerated  ? 


*  Astronomer  Royal  of  Great  Britain,  and  cotemporary  with  Sir  Isaac 
Newton. 


ECLIPSES.  137 

this  acceleration  is  one  of  the  legitimate  effects  of  the 
sun's  disturbing  force,  and  is  so  connected  with  changes 
in  the  eccentricity  of  the  earth's  orbit,  that  the  moon 
will  continue  to  be  accelerated  while  that  eccentricity 
diminishes,  but  when  the  eccentricity  has  reached  its 
minimum  (as  it  will  do  after  many  ages)  and  begins  to 
increase,  then  the  moon's  motion  will  begin  to  be  re- 
tarded, and  thus  her  motions  will  oscillate  forever  about 
a  mean  value.  • 


CHAPTER   V. 

* 

OF  ECLIPSES. 

172.  AN  Eclipse  of  the  moon  happens  when  the  moon 
in  its  revolution  around  the  earth,  falls  into  the  earth's 
shadow.  An  Eclipse  of  the  sun  happens  when  the 
moon  coming  between  the  earth  and  the  sun,  covers 
either  a  part  or  the  whole  of  the  solar  disk. 

The  earth  and  the  moon  being  both  opake  globular 
bodies  exposed  to  the  sun's  light,  they  cast  shadows  op- 
posite to  the  sun  like  any  other  bodies  on  which  the 
sun  shines.  Were  the  sun  of  the  same  size  with  the 
earth  and  the  moon,  then  the  lines  drawn  touching  the 
surface  of  the  sun,  and  the  surface  of  the  earth  or  moon 
(which  lines  form  the  boundaries  of  the  shadow)  would 
be  parallel  to  each  other,  and  the  shadow  would  be  a 
cylinder  infinite  in  length  ;  and  were  the  sun  less  than 
the  earth  or  the  moon,  the  shadow  would  be  an  increas- 
ing cone,  its  narrower  end  resting  on  the  earth  ;  but  as 


172.  When  does  an  eclipse  of  the  moon  happen  ?  When 
does  an  eclipse  of  the  sun  happen  ?  Were  the  sun  of  the  same 
size  with  the  earth  and  moon,  how  would  their  shadows  be  ? 
How  if  less  than  these  bodies  ?  How  are  they  in  fact?  Ex- 
plain by  figure  32 

12* 


138 


THE  MOON. 


the  sun  is  vastly  greater  than  either  of  these  bodies* 
the  shadow  of  each  is  a  cone,  whose  base  rests  on  the 
body  itself,  and  which  comes  to  a  point  or  vertex  at  a 
certain  distance  behind  the  body.  These  several  cases 
are  represented  in  the  following  diagrams. 


173.  It  is  found  by  calculation,  that  the  length  of  the 
moon's  shadow  is,  on  an  average,  just  about  sufficient  to 
reach  to  the  earth,  but  the  moon  is  sometimes  farther 
from  the  earth  than  at  others.  (Art.  166.)  When  she  is 
nearer  than  usual,  the  shadow  reaches  considerably  be- 
yond the  surface  of  the  earth.  Also  the  moon  as  well 
as  the  earth,  is  at  different  distances  from  the  sun  at  dif- 
ferent times,  and  its  shadow  is  longest  when  it  is  far- 
thest from  the  sun.  Now  when  both  these  circumstan- 
ces conspire,  that  is,  when  the  moon  is  in  her  perigee 
and  in  her  aphelion,  her  shadow  extends  nearly  15000 
miles  beyond  the  center  of  ,the  earth,  and  covers  a  space 


173.  How  does  the  moon's  shadow  compare  with  her  dis- 
tance from  the  earth  ?  When  does  her  shadow  extend  farthest 
beyond  the  center  of  the  earth  ?  What  is  the  greatest  breadth 
of  her  shadow  where  it  falls  on  the  surface  of  the  earth  ?  What 
is  the  length  of  the  earth's  shadow  ?  When  only  can  an  eclipse 
of  the  sun  take  place  ?  When  only  can  an  eclipse  of  the  moon 
occur  ?  Explain  from  figure  33.  What  is  the  moon's  Pen- 
umbra ? 


ECLIPSES.  139 

on  the  surface  of  the  earth  170  miles  broad.  The 
earth's  shadow  is  towards  a  million  of  miles  in  length, 
and  more  than  three  and  a  half  times  as  long  as  the  dis- 
tance from  the  earth  to  the  moon ;  and  it  is  also  at  the 
distance  of  the  moon  three  times  as  broad  as  the  moon 
itself.  An  eclipse  of  the  sun  can  take  place  only  at  new 
moon,  when  the  sun  and  moon  meet  in  the  same  part  of 
the  heavens,  for  then  only  can  the  moon  come  between 
us  and  the  sun ;  and  an  eclipse  of  the  moon  can  occur 
only  when  the  sun  and  moon  are  in  opposite  parts  of 
the  heavens,  or  at  full  moon,  for  then  only  can  the  moon 
fall  into  the  shadow  of  the  earth. 

The  nature  of  eclipses  will  be  clearly  understood  from 
the  following  representation.     This  figure  exhibits  the 

Fig.  33. 


relative  position  of  the  sun,  the  earth,  and  the  moon, 
both  in  a  solar  and  in  a  lunar  eclipse.  -  It  is  evident  from 
the  figure,  that  if  a  spectator  were  situated  where  the 
moon's  shadow  strikes  the  earth,  the  moon  would  cut  off 
from  him  the  view  of  the  sun,  or  the  sun  would  be  to- 
tally eclipsed.  Or,  if  he  were  within  a  certain  distance 
of  the  shadow  on  either  side,  the  moon  would  be  partly 
between  him  and  the  sun,  and  would  intercept  from 
him  more  or  less  of  the  sun's  light,  according  as  he  was 
nearer  to  the  shadow  or  farther  from  it.  If  he  were  at 
c,  or  «,  he  would  just  see  the  moon  entering  upon  the 


140  THE  MOON. 

sun's  disk  ;  if  he  were  nearer  the  shadow  than  either  of 
these  points,  he  would  have  a  portion  of  the  sun's  light 
cut  oft*  from  his  view,  and  the  moment  he  entered  the 
shadow  itself,  he  would  lose  sight  of  the  sun.  To  all 
places  between  c  or  d  and  the  shadow,  the  sun  would 
cast  a  partial  shadow  of  the  moon,  growing  deeper  and 
deeper  as  it  approached  the  true  shadow.  This  partial 
shadow  is  called  the  moon's  Penumbra.  In  like  man- 
ner, as  the  moon  approaches  the  earth's  shadow  in  a  lu- 
nar eclipse,  as  soon  as  she  arrives  at  «,  the  earth  begins 
to  intercept  from  her  a  portion  of  the  sun's  light,  or  she 
falls  into  the  earth's  penumbra.  She  continues  to  lose 
more  and  more  of  the  sun's  light  as  she  draws  near  to 
the  shadow,  and  hence  her  disk  becomes  gradually  ob- 
scured, until  it  enters  the  shadow,  where  the  sun's  light 
is  entirely  lost. 

174.  As  the  sun  and  earth  are  both  situated  in  the 
plane  of  the  ecliptic,  if  the  moon1  also  revolved  around 
the  earth  in  this  plane,  we  should  have  a  solar  eclipse  at 
every  new  moon,  and  a  lunar  eclipse  at  every  full 
moon  ;  for  m  the  former  case  the  moon  would  come  di- 
rectly between  us  and  the  sun,  and  in  the  latter  case, 
the  earth  would  come  directly  between  the  sun  and  the 
moon.  But  the  moon's  path  is  inclined  to  the  ecliptic 
about  5°,  and  the  center  of  the  moon  may  be  all  this 
distance  from  the  center  of  the  sun,  at  new  moon,  and 
the  same  distance  from  the  center  of  the  earth's  shadow 
at  full  moon.  It  is  true  the  moon  extends  across  her 
path,  one  half  her  breadth  lying  on  each  side  of  it,  and 
the  sun  likewise  reaches  from  the  ecliptic  a  distance 
equal  to  half  his  breadth.  But  these  luminaries  to- 
gether make  but  little  more  than  a  degree,  and  conse- 
quently their  two  semi-diameters  would  occupy  only 


174.  Why  do  we  not  have  a  solar  eclipse  every  new  moon, 
and  a  lunar  eclipse  every  full  moon  ?  Explain  how  eclipses 
occur  only  when  the  sun  is  near  one  of  the  moon's  nodes,  by 
figure  34. 


ECLIPSES.  141 

about  half  a  degree  of  the  five  degrees  from  one  orbit 
to  the  other.  Also  the  earth's  shadow  where  the  moon 
crosses  it  extends  from  the  ecliptic.,  less  than  three 
fourths  of  a  degree,  so  that  the  semi-diameter  of  the 
moon  and  of  the  earth's  shadow,  would  together  reach 
but  little  way  across  the  space  that  may  in  certain  cases 
separate  the  two  luminaries  from  each  other  when  they 
are  in  opposition.  Thus  suppose  we  could  take  hold 
of  the  circle  in  the  figure  that  represents  the  moon's 
orbit,  (Fig.  31,)  and  lift  the  moon  up  five  degrees  above 
the  plane  of  the  paper,  it  is  evident  that  the  moon 
as  seen  from  the  earth,  would  appear  in  the  heavens 
five  degreess  above  the  sun,  and  of  course  would  cut  off 
none  of  his  light,  and  that  the  moon  at  the  full  would 
pass  the  shadow  of  the  earth  five  degrees  below  it,  and 
would  suffer  no  eclipse.  But  in  the  course  of  the  sun's 
apparent  revolution  around  the  earth  once  a  year,  he  is 
successively  in  every  part  of  the  ecliptic ;  consequently, 
the  conjunctions  and  oppositions  of  the  sun  and  moon 
may  occur  at  any  part  of  the  ecliptic,  and  of  course  at 
the  two  points  where  the  moon's  orbit  crosses  the  eclip- 
tic, that  is,  at  the  nodes,  for  the  sun  must  necessarily 
come  to  each  of  these  nodes  once  a  year.  If  then  the 
moon  overtakes  the  sun  just  as  she  is  crossing  his  path, 

Fig.  34. 


she  will  hide  more  or  less  of  his  disk  from  us.  Since, 
also,  the  earth's  shadow  is  always  directly  opposite  to 
the  sun,  if  the  sun  is  at  one  of  the  nodes,  the  shadow 


142  THE  MOON. 

must  extend  in  the  direction  of  the  other  node,  so  as  to 
lie  directly  across  the  moon's  path,  and  if  the  moon  over- 
takes it  there,  she  will  pass  through  it  and  be  eclipsed. 
Thus  in  figure  34,  let  BN  represent  the  sun's  path,  and 
AN  the  moon's,  N  being  the  place  of  the  node  ;  then  it  v 
evident  that  if  the  two  luminaries  at  new  moon  be  s 
far  from  the  node,  that  the  distance  between  their  centers 
is  greater  than  their  semi-diameters,  no  eclipse  can  hap- 
pen ;  but  if  that  distance  is  less  than  this  sum  as  at 
JE,  F,  then  an  eclipse  will  take  place,  but  if  the  position 
be  as  at  C,  D,  the  two  bodies  will  just  touch  one  another. 
If  A  denote  the  earth's  shadow  instead  of  the  sun,  the 
same  illustration  will  apply  to  an  eclipse  of  the  moon. 

175.  Since  bodies  are  defined  to  be  in  conjunction 
when  they  are  in  the  same  part  of  the  heavens,  and  to 
be  in  opposition  when  they  are  in  opposite  parts  of  the 
heavens,  it  may  not  appear  how  the  sun  and  moon  can 
be  in  conjunction  as  at  A  and  B,  when  they  are  still  at 
some  distance  from  each  other.     But  it  must  be  recol- 
lected that  bodies  are  in  conjunction  when  they  have  the 
same  longitude,  in  which  case  they  are  both  situated  in 
the  same  great  circle  perpendicular  to  the  ecliptic,  that 
is,  in  the  same  secondary  to  the  ecliptic.     One  of  the 
bodies  may  be  much  farther  from  the  ecliptic  than  the 
other  ;  still,  if  the  same  secondary  to  the  ecliptic  passes 
through  them  both,  they  will  be  in  conjunction  or  oppo- 
sition. 

176.  In  a  total  eclipse  of  the  moon,  its  disk  is  still 
visible,  shining  with  a  dull  red  light.     This  light  cannot 
be  derived  directly  from  the  sun,  since  the  view  of  the 
sun  is  completely  hidden  from  the  moon  ;  nor  by  reflex- 
ion from   the  earth,  since  the  illuminated  side  of  the 


175.  Is  it  necessary  for  two  bodies  to  be  precisely  together 
in  order  to  be  in  conjunction  ? 

176.  Why  is  the  disk  of  the  moon  still  visible  in  a  total 
eclipse  of  the  moon  ? 


ECLIPSES.  143 

earth  is  wholly  turned  from  the  moon ;  but  it  is  owing 
to  refraction  from  the  earth's  atmosphere^  by  which  a 
few  scattered  rays  of  the  sun  are  bent  round  into  the 
earth's  shadow  and  conveyed  to  the  moon,  sufficient  in 
number  to  afford  the  feeble  light  in  question. 

177.  It  is  impossible  fully  to  understand  the  method 
vf  calculating  eclipses,  without  a  knowledge  of  trigo- 
nometry ;  still  it  is  not  difficult  to  form  some  general  no- 
tion of  the  process.     It  may  be  readily  conceived  that, 
by  long  continued  observations  on  the  sun  and  moon, 
the  exact  places  which  they  will  occupy  in  the  heavens 
at  any  future  times,  may  be  forseen  and  laid  down  in 
tables  of  the  sun  and  moon's  motions ;  that  we  may  thus 
ascertain  by  inspecting  the  tables  the  exact  instant  when 
these  two  bodies  will  appear  together  in  the  heavens,  or 
be  in  conjunction,  and  when  they  will  be  180°  apart, 
or  in  opposition.     Moreover,  since  the  exact  place  of  the 
moon's  node  among  the  stars  at  any  particular  time  is 
known  to  astronomers,  it  cannot  be  difficult  to  determine 
when  the  new  or  full  moon  occurs  in  the  same  part  of 
the  heavens  as  that  where  the  node  is  projected  as  seen 
from  the  earth.     In  short,  as  astronomers  can  easily  de- 
termine what  will  be  the  relative  position  of  the  sun, 
the  moon,  and  the  moon's  nodes  for  any  given  time, 
they  can  tell  when  these  luminaries  will  meet  so  near 
the  node  as  to  produce  an  eclipse  of  the  sun,  or  when 
they  will  be  in  opposition  so  near  the  node  as  to  produce 
an  eclipse  of  the  moon. 

178.  Let  us  endeavor  to  form  a  just  conception  of  the 
manner  in  which  these  three  bodies,  the  sun,  the  earth, 
and  the  moon,  are  situated  with  respect  to  each  other  at 
the  time  of  a  solar  eclipse.     First,  suppose  the  conjunction 
to  take  place  at  the  node.     Then  the  straight  line  which 
connects  the  center  of  the  sun  and  the  earth,  also  passes 


177.  What  science  must  be  known  in  order  fully  to  under- 
stand the  mode  of  calculating  eclipses  ?  Explain  the  general 
principles  of  the  calculation. 


144  THE  MOON. 

through  the  center  of  the  moon,  and  coincides  with  the 
axis  of  its  shadow ;  and,  since  the  earth  is  bisected  by 
the  plane  of  the  ecliptic,  the  shadow  would  traverse  the 
earth  in  the  direction  of  the  terrestrial  ecliptic,  from 
west  to  east,  passing  over  the  middle  regions  of  the 
earth.  Here  the  diurnal  motion  of  the  earth  being  in 
the  same  direction  with  the  shadow,  but  with  a  less  ve- 
locity, the  shadow  will  appear  to  move  with  a  speed 
equal  only  to  the  difference  between  the  two.  Secondly, 
suppose  the  moon  is  on  the  north  side  of  the  ecliptic  at 
the  time  of  conjunction,  and  moving  towards  her  de- 
scending node,  and  that  the  conjunction  takes  place 
as  far  from  the  node  as  an  eclipse  can  happen.  The 
shadow  will  not  fall  in  the  plane  of  the  ecliptic,  but 
a  little  northward  of  it,  so  as  just  to  graze  the  earth 
near  the  pole  of  the  ecliptic.  The  nearer  the  conjunc- 
tion comes  to  the  node,  the  farther  the  shadow  will  fall 
from  the  pole  of  the  ecliptic  towards  the  equatorial  re- 
gions. 

179.  The  leading  particulars  respecting  an  ECLIPSE 
OF  THE  SUN,  are  ascertained  very  nearly  like  those  of  a 
lunar  eclipse.  The  shadow  of  the  moon  travels  over  a 
portion  of  the  earth,  as  the  shadow  of  a  small  cloud,  seen 
from  an  eminence  in  a  clear  day,  rides  along  over  hills 
and  plains.  Let  us  imagine  ourselves  standing  on  the 
moon ;  then  we  shall  see  the  earth  partially  eclipsed  by 
the  shadow  of  the  moon,  in  the  same  manner  as  we 
now  see  the  moon  eclipsed  by  the  earth's  shadow. 

But,  although  the  general  characters  of  a  solar  eclipse 
might  be  investigated  on  these  principles,  so  far  as  re- 
spects the  earth  at  large,  yet  as  the  appearances  of  the 
same  eclipse  of  the  sun  are  very  different  at  different 
places  on  the  earth's  surface,  it  is  necessary  to  calculate 


178.  Explain  the  relative  position  of  the  sun,  the  earth,  and 
the  moon,  in  a  solar  eclipse.  Explain  the  circumstances  when 
the  conjunction  takes  place  at  the  node,  and  when  it  occurs  at 
a  distance  from  the  node. 


ECLIPSES.  145 

its  peculiar  aspects  for  each  place  separately,  a  circum- 
stance which  makes  the  calculation  of  a  solar  eclipse 
much  more  complicated  and  tedious  than  of  an  eclipse 
of  the  moon.  The  moon,  when  she  enters  the  shadow 
of  the  earth,  is  deprived  of  the  light  of  the  part  immer- 
sed, and  that  part  appears  black  alike  to  all  places  where 
the  moon  is  above  the  horizon.  But  it  is  not  so  with  a 
solar  eclipse.  We  do  not  see  this  by  the  shadow  cast 
on  the  earth,  as  we  should  do  if  we  stood  on  the  moon, 
but  by  the  interposition  of  the  moon  between  us  and  the 
sun ;  and  the  sun  may  be  hidden  from  one  observer 
while  he  is  in  full  view  of  another  only  a  few  miles  dis- 
tant. Thus,  a  small  insulated  cloud  sailing  in  a  clear 
sky,  will,  for  a  few  moments,  hide  the  sun  from  us,  and 
from  a  certain  space  near  us,  while  all  the  region  around 
is  illuminated. 

We  have  compared  the  motion  of  the  moon's  shadow 
over  the  surface  of  the  earth  to  that  of  a  cloud  ;  but  its 
velocity  is  incomparably  greater.  The  mean  motion  of 
the  moon  around  the  earth  is  about  33'  per  hour ;  but 
33'  of  the  moon's  orbit  is  2280  miles,  and  the  shadow 
moves  of  course  at  the  same  rate,  or  2280  miles  per 
hour,  traversing  the  entire  disk  of  the  earth  in  less  than 
four  hours. 

180.  The  diameter  of  the  moon's  shadow  where  it 
eclipses  the  earth  can  never  exceed  170  miles,  and  com- 
monly falls  much  short  of  that ;  and  the  greatest  por- 
tion of  the  earth's  surface  ever  covered  by  the  moon's 
penumbra  is  about  4393  miles. 

181.  The  apparent  diameter  of  the  moon  is  sometimes 
larger  than  that  of  the  sun,  sometimes   smaller,  and 


179.  How  are  the  leading  particulars  of  an  eclipse  of  the  sun 
ascertained  ?  How  illustrated  by  the  motion  of  a  cloud  ?  In 
what  respects  does  the  calculation  of  a  solar  differ  from  that  of 
a  lunar  eclipse  ?  How  does  the  shadow  of  the  moon  cempare 
with  that  of  a  cloud  in  velocity  ? 

13 


146 


THE    MOON. 


sometimes  exactly  equal  to  it.  Suppose  an  observer 
placed  on  the  right  line  which  joins  the  centers  of  the 
sun  and  moon  ;  if  the  apparent  diameter  of  the  moon  is 
greater  than  that  of  the  sun,  the  eclipse  will  be  total.  If 
the  two  diameters  are  equal,  the  moon's  shadow  just 
reaches  the  earth,  and  the  sun  is  hidden  but  for  a  mo- 
ment from  the  view  of  spectators  situated  in  the  line 
which  the  vertex  of  the  shadow  describes  on  the  surface 
of  the  earth.  But  if,  as  happens  when  the  moon  comes 
to  her  conjunction  in  that  part  of  her  orbit  which  is  to- 
wards her  apogee,  the  moon's  diameter  is  less  than  the 
sun's,  then  the  observer  will  see  a  ring  of  the  sun  en- 
circling the  moon,  constituting  an  Annular  Eclipse,  as  in 
figure  35. 

Fig.  35. 


180.  What  cannot  the    diameter  of  the  moon's  shadow 
where  it  eclipses  the  earth,   exceed  ?     What  is  the  greatest 
portion  of  the  earth's  surface  ever  covered  by  the  moon's  pe- 
numbra ? 

181 .  How  does  the  moon's  apparent  diameter  compare  with 
the  sun'*  ?    When  will  the  eclipse  b©  total,  and  when  annular  ? 


ECLIPSES.  147 

182.  Eclipses  of  the  sun  are  modified  by  the  eleva- 
tion of  the  moon  above  the  horizon,  since  its  apparerft 
diameter  is  augmented  as  its  altitude  is  increased.     This 
effect,  combined  with  that  of  parallax,  may  so  increase 
or  diminish  the  apparent  distance  between  the  centers  of 
the  sun  and  moon,  that  from  this  cause  alone,  of  two 
observers  at  a  distance  from  each  other,  one  might  see 
an  eclipse  which  was  not  visible  to  the  other.     If  the 
horizontal  diameter  of  the  moon  differs  but  little  from 
the  apparent  diameter  of  the  sun,  the  case  might  occur 
where  the  eclipse   would  be  annular  over  the  places 
where  it  was  observed  morning  and  evening,  tyit  total 
where  it  was  observed  at  mid-day. 

The  earth  in  its  diurnal  revolution  and  the  moon's 
shadow  both  move  from  west  to  east,  but  the  shadow 
moves  faster  than  the  earth  ;  hence  the  moon  overtakes 
the  sun  on  its  western  limb  and  crosses  it  from  west  to 
east.  The  excess  of  the  apparent  diameter  of  the  moon 
above  that  of  the  sun  in  a  total  eclipse  is  so  small,  that 
total  darkness  seldom  continues  longer  than  four  minutes, 
and  can  never  continue  so  long  as  eight  minuutes.  An 
annular  eclipse  may  last  12m.  24s. 

183.  Eclipses  of  the  sun  are  more  frequent  than  those 
of  the  moon.     Yet  lunar  eclipses  being  visible  to  every 
part  of  the  terrestrial  hemisphere  opposite  to  the  sun,, 
while  those  of  the  sun  are  visible  only  to  the  small  por- 
tion of  the  hemisphere  on  which  the  moon's  shadow 
falls,  it  happens  that  for  any  particular  place  on  the 
earth,  lunar  eclipses  are  more  frequently  visible  than 
solar.     In  any  year,  the  number  of  eclipses  of  both  lu- 


182.  How  are  eclipses  of  the  sun  modified  by  the  elevation 
of  the  moon  above  the  horizon  ?     How  might  the  same  eclipse 
appear  total  to  one   observer  and  annular  to  another  ?     How 
long  cin  total  darkness  continue  in  a  solar  eclipse  ?    How  long 
may  an  annular  eclipse  last  ? 

183.  Which  are  most  frequent,  solar  or  lunar  eclipses  ?  Why 
does  an  eclipse'of  the  moon  sometimes  happen  at  the  next  full 
moon  after  an  eclipse  of  the  sun  ? 


148  REVOLUTIONS. 

t 

Binaries  cannot  be  less  than  two  nor  more  than  seven : 
the  most  usual  number  is  four,  and  it  is  very  rare  to 
have  more  than  six.  A  total  eclipse  of  the  moon  fre- 
quently happens  at  the  next  full  moon  after  an  eclipse 
of  the  sun.  For  since,  in  an  eclipse  of  the  sun,  the  sun 
is  at  or  near  one  of  the  moon's  nodes,  the  earth's  shadow 
must  be  at  or  near  the  other  node,  and  may  not  have 
passed  far  from  the  node  before  the  moon  overtakes  it. 

184.  In  total  eclipses  of  the  sun,  there  has  sometimes 
been  observed  a  remarkable  radiation  of  light  from  the 
margin  of  the  sun.  This  has  been  ascribed  to  an  illu- 
mination of  the  solar  atmosphere,  but  it  is  with  more 
probability  owing  to  the  zodiacal  light,  which  at  that 
time  is  projected  around  the  sun,  and  which  is  of  such 
dimensions  as  to  extend  far  beyond  the  solar  orb.* 

A  total  eclipse  of  the  sun  is  one  of  the  most  sublime 
and  impressive  phenomena  of  nature.  Among  barbarous 
tribes  it  is  ever  contemplated  with  fear  and  astonish- 
ment, while  among  cultivated  nations  it  is  recognized, 
from  the  exactness  with  which  the  time  of  occurrence 
and  the  various  appearances  answer  to  the  prediction,  as 
affording  one  of  the  proudest  triumphs  of  astronomy. 
By  astronomers  themselves  it  is  of  course  viewed  with 
the  highest  interest,  not  only  as  verifying  their  calcula- 
tions,- but  as  contributing  to  establish  beyond  all  doubt 
the  certainty  of  those  grand  laws,  the  truth  of  which  is 
involved  in  the  result.  During  the  eclipse  of  June, 
1806,  which  was  one  of  the  most  remarkable  on  record, 
the  time  of  total  darkness,  as  seen  by  the  author  of  this 
work,  was  about  mid-day.  The  sky  was  entirely  cloud- 


1 84.  How  is  the  radiation  of  light  around  the  margin  of  the 
sun  in  a  total  eclipse  of  the  sun,  accounted  for  ?  How  have 
eclipses  of  the  sun  been  regarded  among  barbarous  tribes  ? 
How  among  civilized  nations  1  How  by  astronomers  ?  Givo 
some  account  of  the  great  eclipse  of  1806. 

*  See  an  excellent  description  and  delineation  of  this  appearance  as 
it  was  exhibited  in  the  eclipse  of  1806,  in  the  Transactions  ol  the  Al- 
bany Institute,  by  the  late  Chancellor  JDe  Witt 


ECLIPSES  149 

less,  but  -as  the  period  of  total  obscuration  approached,  a 
gloom  pervaded  all  nature.  When  the  sun  was  wholly 
lost  sight  of,  planets  and  stars  came  into  view ;  a  fearful 
pall  hung  upon  the  sky,  unlike  both  to  night  and  to 
twilight ;  and,  the  temperature  of  the  air  rapidly  de- 
clining, a  sudden  chill  came  over  the  earth.  Even  the 
animal  tribes  exhibited  tokens  of  fear  and  agitation. 

185.  The  word  Eclipse  is  derived  from  a  Greek  word, 
(exleiytg,)  which  signifies  to  fail,  to  faint,  or  swoon 
away,  since  the  moon  at  the  period  of  her  greatest 
brightness  falling  into  the  shadow  of  the  earth,  was  im- 
agined by  the  ancients  to  sicken  and  swoon,  as  if  she 
were  going  to  die.  By  some  very  ancient  nations  she 
was  supposed  at  such  times  to  be  in  pain,  and  hence 
lunar  eclipses  were  called  the  labors  of  the  moon,  (Iuna3 
labores ;)  and,  in  order  to  relieve  her  fancied  distress,  they 
lifted  torches  high  in  the  atmosphere,  blew  horns  and 
trumpets,  beat  upon  brazen  vessels,  and  even,  after  the 
eclipse  was  over,  they  offered  sacrifices  to  the  moon. 
The  opinion  also  extensively  prevailed,  that  it  was  in 
the  power  of  witches,  by  their  spells  and  charms,  not 
only  to  darken  the  moon,  but  to  bring  her  down  from 
her  orbit,  and  to  compel  her  to  shed  her  baleful  influences 
upon  the  earth.  In  a  solar  eclipse  also,  especially  when 
total,  the  sun  was  supposed  to  turn  away  his  face  in  ab- 
horrence of  some  atrocious  crime,  that  either  had  been 
perpetrated  or  was  about  to  be  perpetrated,  and  to 
threaten  mankind  with  everlasting  night,  and  the  de- 
struction of  the  world. 

The  Chinese,  who  from  a  very  high  period  of  anti- 
quity have  been  great  observers  of  eclipses,  although 
they  did  not  take  much  notice  of  those  of  the  moon,  re- 
garded eclipses  of  the  sun  in  general  as  unfortunate,  but 
especially  such  as  occurred  on  the  first  day  of  the  year. 


185.  From  what  is  the  word  eclipse  derived  ?  What  ideas 
bad  certain  ancient  nations  respecting  eclipses  ?  With  what 
ceremonies  did  they  observe  them  ?  How  were  eclipses  re- 
garded among  the  Chinese  ? 

13* 


150  THE  MOON. 

These  were  thought  to  forbode  the  greatest  calamities 
to  the  emperor,  who  on  such  occasions  did  not  receive 
the  usual  compliments  of  the  season.  When  an  eclipse 
of  the  sun  was  expected  from  the  predictions  of  their  as- 
^tronomers,  they  made  great  preparation  at  court  for  ob- 
serving it ;  and  as  soon  as  it  commenced,  a  blind  man 
beat  a  drum  and  a  great  concourse  assembled,  and  the 
Mandarins,  or  nobility,  appeared  in  state. 

186.  From  1831  to  1838,  was  a  period  distinguished 
for  great  eclipses  of  the  sun,  in  which  time  there  were  no 
less  than  five,  of  the  most  remarkable  character.  The 
next  total  eclipse  of  the  sun,  visible  in  the  United  States, 
will  occur  on  the  7th  of  August,  1869. 


CHAPTER    VI. 

OF  LONGITUDE. TIDES. 

187.  As  eclipses  of  the  sun  afford  one  of  the  most 
approved  methods  of  finding  the  longitude  of  places,  our 
attention  is  naturally  turned  next  towards  that  subject, 

The  ancients  studied  astronomy  in  order  that  they 
might  read  their  destinies  in  the  stars  :  the  moderns  that 
they  may  securely  navigate  the  ocean.  A  large  portion 
of  the  refined  labors  of  modern  astronomy,  has  been  di- 
rected towards  perfecting  the  astronomical  tables  with 
the  view  of  finding  the  longitude  at  sea, — an  object 
manifestly  worthy  of  the  highest  efforts  of  science,  con- 
sidering the  vast  amount  of  property  and  of  human  life 
involved  in  navigation. 

188.  The  difference  of  longitude  between   two  places, 
may  be  found  by  any  method  by  which  we  can  ascertain 

1S6.  What  recent  period  has  abounded  with  great  eclipses 
of  the  sun  ?  When  will  the  next  total  eclipse  of  the  sun  occur  ? 

1 87.  For  what  purpose  did  the  ancients  study  astronomy  ? 
For  what  purpose  do  the  moderns  study  it  ? 


LONGITUDE.  151 

the  difference  of  their  local  times,  at  the  same  instant  of 
absolute  time. 

As  the  earth  turns  on  its  axis  from  west  to  east,  any 
place  that  lies  eastward  of  another  will  come  sooner  un- 
der the  sun,  or  will  have  the  sun  earlier  on  the  meridian, 
and  consequently,  in  respect  to  the  hour  of  the  day,  will 
be  in  advance  of  the  other  at  the  rate  of  one  hour  for 
every  15°,  or  four  minutes  of  time  for  each  degree.  Thus, 
to  a  place  15°  east  of  Greenwich,  it  is  1  o'clock,  P.  M. 
when  it  is  noon  at  Greenwich;  and  to  a  place  15°  west 
of  that  meridian,  it  is  11  o'clock,  A.  M.  at  the  same  in- 
stant. Hence  the  difference  of  time  at  any  two  places, 
indicates  their  difference  of  longitude. 

189.  The  easiest  method  of  finding  the  longitude  is 
by  means  of  an  accurate  time  piece,  or  chronometer.  Let 
us  set  out  from  London  with  a  chronometer  accurately 
adjusted  to  Greenwich  time,  and  travel  eastward  to  a 
certain  place,  where  the  time  is  accurately  kept,  or  may 
be  ascertained  by  observation.  We  find,  for  example, 
that  it  is  1  o'clock  by  our  chronometer,  when  it  is  2 
o'clock  and  30  minutes  at  the  place  of  observation. 
Hence  the  longitude  is  15  x  1.5=22i°  E.  Had  we  trav- 
elled westward  until  our  chronometer  was  an  hour  and 
a  half  in  advance  of  the  time  at  the  place  of  observa- 
tion, (that  is,  so  much  later  in  the  day,)  our  longitude 
would  have  been  22^°  W.  But  it  would  not  be  neces- 
sary to  repair  to  London  in  order  to  set  our  chronometer 
to  Greenwich  time.  This  might  be  done  at  any  obser- 
vatory, or  any  place  whose  longitude  has  been  accu- 


188.  How  may  the  difference  of  longitude  between  two  pla- 
ces be  found  ?     How  many  degrees  of  longitude  correspond  to 
one  hour  in  time  ?     How  many  minutes  to  one  degree  ? 

189.  Explain  the  method  of  finding  the  longitude  by  the 
chronometer.     To  what  time  is  it  set  ?    How  do  we  ascertain 
the  longitude  of  a  place  by  it  ?     Would  it  be  necessary  to  re- 
pair to  Greenwich  to  regulate  our  chronometer  ?     What  is  said 
oi  the  accuracy  of  some   chronometers  ?     Why  is  not  this 
method  adapted  to  general  use  ? 


152  THE  MOON. 

rately  determined.  For  example,  the  time  at  New  YorR 
is  4h.  56m.  4s.5  behind  that  of  Greenwich.  If,  there- 
fore, we  set  our  chronometer  so  much  before  the  true 
time  at  New  York,  it  will  indicate  the  time  at  Green- 
wich. Moreover,  on  arriving  at  different  places  any 
where  on  the  earth,  whose  longitude  is  accurately  known, 
we  may  learn  whether  our  chronometer  keeps  accurate 
time  or  not,  and  if  not,  the  amount  of  its  error.  Chro- 
nometers have  been  constructed  of  such  an  astonishing 
degree  of  accuracy,  as  to  deviate  but  a  few  seconds  in  a 
voyage  from  London  to  Baffin's  Bay  and  back,  during  an 
absence  of  several  years.  But  chronometers  which  are 
sufficiently  accurate  to  be  depended  on  for  long  voya- 
ges, are  too  expensive  for  general  use,  and  the  means  of 
verifying  their  accuracy  are  not  sufficiently  easy.  More- 
over, chronometers,  by  being  transported  from  one  place 
to  another,  change  their  daily  rate,  or  depart  from  that 
mean  rate  which  they  preserve  at  a  fixed  station,  A 
chronometer,  therefore,  cannot  be  relied  on  for  determin- 
ing the  longitudes  of  places  where  the  greatest  degree  of 
accuracy  is. required,  especially  where  the  instrument  is 
conveyed  over  land,  although  the  uncertainty  attendant 
on  one  instrument  may  be  nearly  obviated  by  employing 
several  and  taking  their  mean  results. 

190.  Eclipses  of  the  sun  and  moon  are  sometimes 
used  for  determining  the  longitude.  The  exact  instant 
of  immersion  or  of  emersion,  or  any  other  definite  mo- 
ment of  the  eclipse  which  presents  itself  to  two  distant 
observers,  affords  the  means  of  comparing  their  difference 
of  time,  and  hence  of  determining  their  difference  of 
longitude.  Since  the  entrance  of  the  moon-  into  the 
earth's  shadow,  in  a  lunar  eclipse,  is  seen  at  the  same 
instant  of  absolute  time  at  all  places  where  the  eclipse 
is  visible,  this  observation  would  be  a  very  suitable  one 
for  finding  the  longitude  were  it  not  that,  on  account  of 


1 90.  Explain  how  to  find  the  longitude  by  eclipses  of  the  sun 
and  moon.  What  objections  are  there  to  this  method,  both  in 
lunar  and  solar  eclipses  ? 


LONGITUDE.  .153 

the  increasing  darkness  of  the  penumbra  near  the  boun  • 
claries  of  the  shadow,  it  is  difficult  to  determine  the  pre 
cise  instant  when  the  moon  enters  the  shadow.  By 
taking  observations  on  the  immersions  of  known  spots 
on  the  lunar  disk,  a  mean  result  may  be  obtained  which 
will  give  the  longitude  with  tolerable  accuracy.  In  an 
eclipse  of  the  sun,  the  instants  of  immersion  and  emer- 
sion may  be  observed  with  greater  accuracy,  although, 
since  these  do  not  take  place  at  the  same  instant  of  ab- 
solute time,  the  calculation  of  the  longitude  from  obser- 
vations on  a  solar  eclipse  are  complicated  and  laborious. 

191.  The  lunar  method  of  finding  the  longitude,  at 
sea,  is  in  many  respects  preferable  to  every  other.  It 
consists  in  measuring  (with  a  sextant)  the  angular  dis- 
tance between  the  moon  and  the  sun,  or  between  the 
moon  and  a  star,  and  then  turning  to  the  Nautical  Alma- 
nac,* and  finding  what  time  it  was  at  Greenwich  when 
that  distance  was  the  same.  The  moon  moves  so  rap- 
idly, that  this  distance  will  not  be  the  same  except  at 
very  nearly  the  same  instant  of  absolute  time.  For  ex- 
ample, at  9  o'clock,  A.  M.,  at  a  certain  place,  we  find  the 
angular  distance  of  the  moon  and  the  sun  to  be  72° ; 
and,  on  looking  into  the  Nautical  Almanac,  we  find  that 
the  time  when  this  distance  was  the  same  for  the  me- 
ridian of  Greenwich  was  1  o'clock,  P.  M . ;  hence  we 
infer  that  the  longitude  of  the  place  is  four  hours,  or  60° 
west. 


191.  Explain  the  lunar  method  of  finding  the  longitude. 
What  measurements  are  made  ?  How  do  we  find  the  corres- 
ponding time  at  Greenwich  ? 


*  The  Nautical  Almanac,  is  a  book  published  annually  by  the  British 
Board  of  Longitude,  containing  various  tables  and  astronomical  infor- 
mation for  the  use  of  navigators.  The  American  Almanac  also  con- 
tains a  variety  of  astronomical  information,  peculiarly  interesting  to  the 
people  of  the  United  States,  in  connexion  with  a  vast  amount  ot 
statistical  matter.  It  is  well  deserving  of  a  place  in  the  library  of  the 
student. 


154  THE  MOON. 

The  Nautical  Almanac  contains  the  true  angular  dis- 
tance of  the  moon  from  the  sun,  from  the  four  large 
planets,  (Venus,  Mars,  Jupiter,  and  Saturn,)  and  from 
nine  bright  fixed  stars,  for  the  beginning  of  every  third 
hour  of  mean  time  for  the  meridian  of  Greenwich  ;  and 
the  mean  time  corresponding  to  any  intermediate  hour, 
may  be  found  by  proportional  parts.* 

192.  It  would  be  a  very  simple  operation  to  determine 
the  longitude  by  Lunar  Distances,  if  the  process  as  de- 
scribed in  the  preceding  article  were  all  that  is  neces- 
sary ;  but  the  various  circumstances  of  parallax,  refrac- 
tion, and  dip  of  the  horizon,  would  differ  more  or  less  at 
the  two  places,  even  were  the  bodies,  whose  distances 
were  taken,  in  view  from  both,  which  is  not  necessarily 
the  case.     The  observations,  therefore,  require  to  be 
reduced  to  the  center  of  the  earth,  being  cleared  of  the 
effects  of  parallax  and  refraction.     Hence,  three  obser- 
vers are  necessary  in  order  to  take  a  lunar  distance  in 
the  most  exact  manner,  viz.  two  to  measure  the  altitudes 
of  the  two  bodies  respectively,  at  the  same  time  that 
the  third  takes  the   angular  distance  between    them. 
The  altitudes  of  the  two  luminaries  at  the  time  of  ob- 
servation must  be  known,  in  order  to  estimate  the  effects 
of  parallax  and  refraction. 

193.  Although  the  lunar  method  of  finding  the  longi- 
tude at  sea  has  many  advantages  over  the  other  meth- 
ods in  use,  yet  it  also  has  its  disadvantages.     One  is,  the 
great  exactness  requisite  in  observing  the  distance  of 
the  moon  from  the  sun  or  star,  as  a  small  error  in  the 
distance  makes  a  considerable  error  in  the  longitude. 
The  moon  moves  at  the  rate  of  about  a  degree  in  two 


192.  What  difficulties  are  there  in  this  method  ?     Why  are 
three  observers  necessary  ? 

193.  What  are  the  objections  to  this  method  ?     What  is  the 
error  of  the  best  tables  now  in  use  ? 

*  See  Bowditch's  Navigator,  Tenth  Ed.  p.  226. 


LONGITUDE.  155 

hours,  or  one  minute  of  space  in  two  minutes  of  time. 
Therefore,  if  we  make  an  error  of  one  minute  in  ob- 
serving the  distance,  we  make  an  error  of  two  minutes 
in  time,  or  30  miles  of  longitude  at  the  equator.  A  sin- 
gle observation  with  the  best  sextant,  may  be  liable  to 
an  error  of  more  than  half  a  minute  ;  but  the  accuracy 
of  the  result  may  be  much  increased  by  a  mean  of  sev- 
eral observations  taken  to  the  east  and  west  of  the  moon. 
The  imperfection  of  the  lunar  tables  was  until  recently 
considered  as  an  objection  to  this  method.  Until  within  a 
few  years,  the  best  lunar  tables  were  frequently  errone- 
ous to  the  amount  of  one  minute,  occasioning  an  error 
of  30  miles.  The  error  of  the  best  tables  now  in  use 
will  rarely  exceed  7  or  8  seconds. 

/  TIDES. 

r~* 

194. (The  tides  are  an  alternate  rising  and  falling  of 

the  waters  of  the  ocean,  at  regular  intervals.  They  have 
a  maximum  and  a  minimum  twice  a  day,  twice  a  month, 
and  twice  a  year.  Of  the  daily  tide,  the  maximum  is 
called  High  tide,  and  the  minimum  Low  tide.  The 
maximum  for  the  month  is  called  Spring  tide,  and  the 
minimum  Neap  tide.  The  rising  of  the  tide  is  called 
Flood  and  its  falling  Ebb  tide. 

Similar  tides,  whether  high  or  low,  occur  on  opposite 
sides  of  the  earth  at  once.  Thus  at  the  same  time  that  it 
is  high  tide  at  any  given  place,  it  is  also  high  tide  on  the 
inferior  meridian,  and  the  same  is  true  of  the  low  tides. 

The  interval  between  two  successive  high  tides  is 
12h.  25m.;  or,  if  the  same  tide  be  considered  as  return- 
ing to  the  meridian,  after  having  gone  around  the  globe, 


194.  What  are  the  tides  ?  When  have  they  a  maximum  and 
a  minimum  ?  Define  the  terms  High  and  Low,  Spring  and 
Neap,  Flood  and  Ebb  tides.  What  two  tides  occur  at  the  same 
time  ?  What  is  the  intervalbetween  two  successive  high  tides  ? 
How  much  later  is  the  tide  of  to-day  than  the  same  tide  of 
yesterday  ?  What  is  the  average  height  of  the  tide  for  the 
whole  globe  ?  To  what  extreme  height  does  it  sometimes  rise  ? 
Have  inland  lakes  and  seas  any  tides  ? 


156  THE  MOON 

its  return  is  about  50  minutes  later  than  it  occurred  on 
the  preceding  day.  In  this  respect,  as  well  as  in  various 
others,  it  corresponds  very  nearly  to  the  motions  of  the 
moon. 

The  average  height  for  the  whole  globe  is  about  2J 
feet ;  or,  if  the  earth  were  covered  uniformly  with  a 
stratum  of  water,  the  difference  between  the  two  diam- 
eters of  the  oval  would  be  5  feet,  or  more  exactly  5  feet 
and  8  inches  ;  but  its  actual  height  at  various  places  is 
very  various,  sometimes  rising  to  60  or  70  feet,  and 
sometimes  being  scarcely  perceptible.  At  the  same 
place  also,  the  phenomena  of  the  tides  are  very  different 
at  different  times. 

Inland  lakes  and  seas,  even  those  of  the  largest  class, 
as  Lake  Superior,  or  the  Caspian,  have  no  perceptible 
tide. 

195.  Tides  are  caused  by  the  unequal  attraction  of 
the  sun  and  moon  upon  different  parts  of  the  earth. 

Suppose  the  projectile  force  by  which  the  earth  is  car- 
ried forward  in  her  orbit,  to  be  suspended,  and  the  earth 
to  fall  towards  one  of  these  bodies,  the  moon,  for  exam- 
ple, in  consequence  of  their  mutual  attraction.  Then, 
if  all  parts  of  the  earth  fell  equally  towards  the  moon, 
no  derangement  of  its  different  parts  would  result,  any 
more  than  of  the  particles  of  a  drop  of  water  in  its  de- 
scent to  the  ground.  But  if  one  part  fell  faster  than  an- 
other, the  different  portions  would  evidently  be  separa- 
ted from  each  other.  Now  this  is  precisely  what  takes 
place  with  respect  to  the  earth  in  its  fall  towards  the 
moon.  The  portions  of  the  earth  in  the  hemisphere 
next  to  the  moon,  on  account  of  being  nearer  to  the 
center  of  attraction,  fall  faster  than  those  in  the  oppo- 
site hemisphere,  and  consequently  leave  them  behind. 
The  solid  earth,  on  account  of  its  cohesion,  cannot  obey 


195.  State  the  cause  of  the  tides.  What  would  be  the  con- 
sequence were  the  earth  abandoned  to  the  force  exerted  by 
the  moon  alone  ? 


TIDES. 


157 


this  impulse,  since  all  its  different  portions  constitute 
one  mass,  which  is  acted  on  in  the  same  manner  as 
though  it  were  all  collected  in  the  center ;  but  the  wa- 
ters on  the  surface,  moving  freely  under  this  impulse, 
endeavor  to  desert  the  solid  mass  and  fall  towards  the 
tnoon.  For  a  similar  reason  the  waters  in  the  opposite 
hemisphere  falling  less  towards  the  moon  than  the  solid 
earth  are  left  behind,  or  appear  to  rise  from  the  center 
of  the  earth. 

196.  Let  DEFG  (Fig.  36,)  represent  the  globe  ;  and, 
for  the  sake  of  illustrating  the  principle,  we  will  sup- 
pose the  waters  entirely  to  cover  the  globe  at  a  uniform 
depth.  Let  defg  represent  the  solid  globe,  and  the  cir- 

Fig.  3G. 


cular  ring  exterior  to  it,  the  covering  of  waters.  Let  C 
be  the  center  of  gravity  of  the  solid  mass,  A  that  of  the 
hemisphere  next  to  the  moon,  (for  the  center  of  gravity 
of  a  ring  is  within  the  ring,)  and  B  that  of  the  remoter 
hemisphere.  Now  the  force  of  attraction  exerted  by 
the  moon,  acts  in  the  same  manner  as  though  the  solid 
mass  were  all  concentrated  in  C,  and  the  waters  of  each 
hemisphere  at  A  and  B  respectively  ;  and  (the  moon  be- 


1 96.  Explain  the  tides  upon  the  doctrine  of  the  center  of 
gravity.  Where  would  the  tide-wave  always  be  seen  were  it 
not  for  impediments  ?  What  are  these  ? 

14 


158  THE    MOON. 

ing  supposed  above  E)  it  is  evident  that  A  will  tend  to 
leave  C,  and  C  to  leave  B  behind.  The  same  must  evi- 
dently be  true  of  the  respective  portions  of  matter,  of 
which  these  points  are  the  centers  of  gravity.  The  wa- 
ters of  the  globe  will  thus  be  reduced  to  an  oval  shape, 
being  elongated  in  the  direction  of  that  meridian  which 
is  under  the  moon,  and  flattened  in  the  intermediate 
parts,  and  most  of  all  at  points  ninety  degrees  distant 
from  that  meridian. 

Were  it  not,  therefore,  for  impediments  which  prevent 
the  force  from  producing  its  full  effects,  we  might  expect 
to  see  the  great  tide-wave,  as  the  elevated  crest  is  called, 
ahvays  directly  beneath  the  moon,  attending  it  regularly 
around  the  globe.  But  the  inertia  of  the  waters  pre- 
vents their  instantly  obeying  the  moon's  attraction,  and 
the  friction  of  the  waters  on  the  bottom  of  the  ocean, 
still  farther  retards  its  progress.  It  is  not  therefore  until 
several  hours  (differing  at  different  places)  after  the 
moon  has  passed  the  meridian  of  a  place,  that  it  is  high 
tide  at  that  place. 

197.  The  sun  has  a  similar  action  to  the  moon,  but 
only  one  third  as  great.  On  account  of  the  great  mass 
of  the  sun  compared  with  that  of  the  moon,  we  might 
suppose  that  his  action  in  raising  the  tides  would  be 
greater  than  that  of  the  moon  ;  but  the  nearness  of  the 
moon  to  the  earth  more  than  compensates  for  the  sun's 
greater  quantity  of  matter.  Let  us,  however,  form  a  just 
conception  of  the  advantage  which  the  moon  derives 
from  her  proximity.  It  is  not  that  her  actual  amount  of 
attraction  is  thus  rendered  greater  than  that  of  the  sun  ; 
but  it  is  that  her  attraction  for  the  different  parts  of  the 
earth  is  very  unequal,  while  that  of  the  sun  is  nearly 
uniform.  It  is  the  inequality  of  this  action,  and  not  the 
absolute  force,  that  produces  the  tides.  The  diameter  of 
the  earth  is  ^  of  the  distance  of  the  moon,  while  it  is 
less  than  of  the  distance  of  the  sun. 


197.  Explain  the  action  of  the  sun  in  raising  the  tide  ?   Why 
is  its  effect  less  than  that  of  the  moon  ? 


19* 


TIDES.  159 


Having  now  learned  the  general  cause  of  the 
tides,  we  will  next  attend  to  the  explanation  of  particu- 
lar phenomena. 

The  Spring  tides,  or  those  which  rise  to  an  unusual 
height  twice  a  ntonth,  are  produced  by  the  sun  and 
moon's  acting  together ;  and  the  Neap  tides,  or  those 
which  are  unusually  low  twice  a  month,  are  produced 
by  the  sun  and  moon's  acting  in  opposition  to  each 
other.  The  Spring  tides  occur  at  the  syzigies:  the 
Neap  tides  at  the  quadratures.  At  the  time  of  new  moon, 
the  sun  and  moon  both  being  on  tli£  same  side  of  the 
earth,  and  acting  upon  it  in  the  same  line,  their  actions 
conspire,  and  the  sun  may  be  considered  as  adding  so 
much  to  the  force  of  the  moon.  We  have  already  ex- 
plained how  the  moon  contributes  to  raise  a  tide  on  the 
opposite  side  of  the  earth.  But  the  sun  as  well  as  the 
moon  raises  its  own  tide-wave,  which,  at  new  moon, 
coincides  with  the  lunar  tide-wave.  At  full  moon,  also, 
the  two  luminaries  conspire  in  the  same  way  to  raise 
the  tide ;  for  we  must  recollect  that  each  body  contri- 
butes to  raise  the  tide  on  the  opposite  side  of  the  earth 
as  well  as  on  the  side  nearest  to  it.  At  both  the  con- 
junctions and  oppositions,  therefore,  that  is,  at  the  syzi- 
gies, we  have  unusually  high  tides.  But  here  also  the 
maximum  effect  is  not  at  the  moment  of  the  syzigies, 
but  36  hours  afterwards. 

At  the  quadratures,  the  solar  wave  is  lowest  where  the 
lunar  wave  is  highest ;  hence  the  low  tide  produced  by 
the  sun  is  subtracted  from  high  water  and  produces  the 
Neap  tides.  Moreover,  at  the  quadratures  the  solar 
wave  is  highest  where  the  lunar  wave  is  lowest,  and 
hence  is  to  be  added  to  the  height  of  low  water  at  the 
time  of  Neap  tides.  Therefore  the  difference  between 
high  and  low  water  is  only  about  half  as  great  at  Neap 
tide  as  at  Spring  tide. 


198.  What  is  the  cause  of  the  Springtides  ?  Also  of  the 
Neap  tides  1  How  long  after  the  syzigies  does  the  highest 
tide  occur  ? 


160  THE  MOON 

199.  The  variations  of  distance  in  the  sun  are  not 
great  enough  to  influence  the  tides  very  materially,  but 
the  variations  in  the  moon's  distance  have  a  striking 
effect.     The  tides  which  happen  when  the  rnoon  is  in 
perigee,  are  considerably  greater  than  when  she  is  in 
apogee  ;  and  if  she  happens  to  be  in  perigee  at  the  time 
of   the   syzigies,   the    Spring   tide   is  unusually   high. 
When  this  happens  at  the  equinoxes,  the  highest  tides 
of  the  year  are  produced. 

200.  The  declinations  of  the  sun  and  moon  have  a 
considerable  influence  on  the  height  of  the  tide.     When 
the  moon,  for  example,  has  no  declination,  or  is  in  the 


equator,  as  in  figure  37,*  the  two  tides  will  be  exactly 
equal  on  opposite  sides  of  the  meridian  in  the  same 
parallel.  Thus  a  place  in  the  parallel  TT'  will  have 


199.  How  do  the  variations  in  the  moon's  distance  from  the 
earth  affect  the  tides  ?  How  are  the  tides  when  the  moon  is  in 
perigee  ?  How  when  she  in  apogee  ?  When  are  the  highest 
tides  of  the  year  produced  ? 


*  Diagrams  like  these  are  apt  to  mislead  the  learner,  by  exhibiting  the 
protuberance  occasioned  by  the  tides  as  much  greater  than  the  reality. 
We  must  recollect  that  it  amounts,  at  the  highest,  to  only  a  very  few 
feet  in  eight  thousand  miles.  Were  the  diagram,  therefore,  drawn  in 
just  proportions,  the  alteration  of  figure  produced  by  the  tides  would 
be  wholly  insensible. 


TIDES. 


161 


the  height  of  one  tide  T2  and  the  other  tide  T'3. 
The  tides  are  in  this  case  greatest  at  the  equator,  and 
diminish  gradually  to  the  poles,  where  it  will  be  low 
water  during  the  whole  day.  When  the  moon  is 
on  the  north  side  of  the  equator,  as  in  figure  38,  at 
her  greatest  northern  declination,  a  place  describing 
the  parallel  TT  will  have  T'3  for  the  height  of  the 

Fig.  38. 


tide  when  the  moon  is  on  the  superior  meridian,  and  T2 
for  the  height  at  the  same  time  on  the  inferior  me- 
ridian. Therefore,  all  places  north  of  the  equator  will 
have  the  highest  tide  when  the  moon  is  above  the  hor- 
izon, and  the  lowest  when  she  is  below  it ;  the  differ- 
ence of  the  tides  diminishing  towards  the  equator,  where 
they  are  equal.  In  like  manner,  (the  moon  being  still 
at  M,  Fig.  38,  that  is,  having  northern  declination,) 
places  south  of  the  equator  have  the  highest  tides  when 
the  moon  is  below  the  horizon, -and  the  lowest  when  she 
is  above  it.  The  circumstances  are  all  reversed  when 
the  moon  is  south  of  the  equator. 

201.  The  motion  of  the  tide- wave,  it  should  be  re- 
marked, is  not  a.  progressive  motion,  but  a  mere  undula- 
tion, and  is  to  be  carefully  distinguished  from  the  cur- 


200  Explain  the  effect  of  the  declinations  of  the  sun  and 
moon  upon  the  tides.  How  will  the  upper  and  lower  tides  cor- 
respond when  the  moon  is  in  the  equator  ?  How  when  the 
moon  is  north  of  the  equator  ?  Explain  by  figures  37,  38. 

14* 


162  THE  MOON. 

rents  to  which  it  gives  rise.  If  the  ocean  completely 
covered  the  earth,  the  sun  and  moon  being  in  the  equa- 
tor, the  tide-wave  would  travel  at  the  same  rate  as  the 
earth  on  its  axis.  Indeed,  the  correct  way  of  conceiv- 
ing of  the  tide-wave,  is  to  consider  the  moon  at  rest, 
and  the  earth  in  its  rotation  from  west  to  east,  as  bringing 
successive  portions  of  water  under  the  moon,  which 
portions  being  elevated  successively  at  the  same  rate  as 
the  earth  revolves  on  its  axis,  have  a  relative  motion 
westward  in  the  same  degree. 

202.  The  tides  of  rivers,  narroib  bays,  and  shores 
far  from  the  main  body  of  the  ocean,  are  not  produced 
in  those  places  by  the  direct  action  of  the  sun  and  moon, 
but  are  subordinate  waves  propagated  from  the  great 
tide-wave. 

Lines  drawn  through  all  the  adjacent  parts  of  any 
tract  of  water,  which  have  high  water  at  the  same  time, 
are  called  cotidal  lines.  We  may,  for  instance,  draw  a 
line  through  all  places  in  the  Atlantic  Ocean  which 
have  high  tide  in  a  given  day  at  1  o'clock,  and  another 
through  all  places  which  have  high  tide  at  2  o'clock. 
The  cotidal  line  for  any  hour  may  be  considered  as  rep- 
resenting the  summit  or  ridge  of  the  tide-wave  at  that 
time ;  and  could  the  spectator,  detached  from  the  earth, 
perceive  the  summit  of  the  wave,  he  woulclsee  it  travel- 
ing round  the  earth  in  the  open  ocean  once  in  twenty- 
four  hours,  followed  by  another  twelve  hours  distant, 
and  both  sending  branches  into  rivers,  bays,  and  other 
openings  into  the  main  land.  These  latter  are  called 
Derivative  tides,  while  those  raised  directly  by  the  ac- 
tion of  the  sun  and  moon,  are  called  Primitive  tides. 


201.  Is  the  motion  of  the  tide-wave  progressive?     if  the 
ocean  completely  covered  the  earth  and  the  sun  and  moon  were 
in  the  equator,  how  would  the  tide-wave  travel  ?    What  is  trie 
most  correct  way  of  conceiving  of  the  tide-wave  ? 

202.  How  are  the  tides  of  rivers,  &c.  produced  ?     Define 
cotidal  lines.     What  does  the  cotidai  line  for  any  hour  repre- 
sent ?     Distinguish  between  Primitive  and  Derivative  tides. 


TIDES.  163 

The  velocity  with  which  the  wave  moves,  will 
depend  on  various  circumstances,  but  principally  on  the 
depth,  and  probably  on  the  regularity  of  the  channel. 
If  the  depth  be  nearly  uniform,  the  cotidal  lines  will  be 
nearly  straight  and  parallel.  But  if  some  parts  of  the 
channel  are  deep  while  others  are  shallow,  the  tide  will 
be  detained  by  the  greater  friction  of  the  shallow  places, 
and  the  cotidal  lines  will  be  irregular.  The  direction 
also  of  the  derivative  tide,  may  be  totally  different  from 
that  of  the  primative.  Thus,  (Fig.  39,)  if  the  great 

Fig.  39. 


tide-wave,  moving  from  east  to  west,  be  represented  by 
the  lines  1,  2,  3,  4,  the  derivative  tide  which  is  propa- 
gated up  a  river  or  bay,  will  be  represented  by  the  co- 
tidal  lines  3,  4,  5,  6,  7.  Advancing  faster  in  the  channel 
than  next  the  bank,  the  tides  will  lag  behind  towards 
the  shores,  and  the  cotidal  lines  will  take  the  form  of 
curves  as  represented  in  the  diagram. 


203-  On  what  will  the  velocity  of  the  tide- wave  depend  ? 
"What  circumstances  will  retard  it  ?     Explain  figure  39. 


164  THE  MOON.  ^ 

204.  On  account  of  the  retarding  influence  of  shoals, 
and  an  uneven,  indented  coast,  the  tide-wave  travels 
more  slowly  along  the  shores  of  an  island   than  in  the 
neighbouring  sea,  assuming  convex  figures  at  a  little  dis- 
tance from  the  island  and  on  opposite  sides  of  it.     These 
convex  lines  sometimes  meet  and  become  blended  in 
such  a  manner  as  to  create  singular  anomalies  in  a  sea 
much  broken  by  islands,  as  well  as  on  coasts  indented 
with  numerous  bays  and  rivers.     Peculiar  phenomena 
are  also  produced,  when  the  tide  flows  in  at  opposite 
extremities  of  a  reef  or  island,  as  into  the  two  opposite 
ends  of  Long  Island  Sound.     In  certain  cases  a  tide- 
wave  is  forced  into  a  narrow  arm  of  the  sea,  and  pro- 
duces very  remarkable  tides.     The  tides  of  the  Bay  of 
Fundy  (the  highest  in  the  world)   sometimes  rise   to 
the  height  of  60  or  70  feet ;  and  the  tides  of  the  rivei 
Severn,  near  Bristol  in  England,  rise  to  the  height  of  40 
feet. 

205.  The  Unit  of  Altitude  of  any  place,  is  the  height 
of  the  maximum  tide   after  the  syzigies,  being  usually 
about  36  hours  after  the  new  or  full  moon.     But  as  the 
amount  of  this  tide  would  be  affected  by  the  distance  of 
the  sun  and  moon  from  the  earth,  and  by  their  declina- 
tions, these  distances  are  taken  at  their  mean  value,  and 
the  luminaries  are  supposed  to  be  in  the  equator ;  the 
observations  being  so  reduced  as  to  conform  to  these  cir- 
cumstances.    The  unit  of  altitude  can  be  ascertained 
by  observation  only.     The  actual  rise  of  the  tide  de- 
pends much  on  the  strength  and  direction  of  the  wind. 
When  high  winds  conspire  with  a  high  flood  tide,  as  is 
frequently  the  case  near  the  equinoxes,  the  tide  often 


204.  How  does  the  tide-wave  travel  along  the  shores  of  an 
island  ?  How  are  the  great  tides  of  the  Bay  of  Fundy  accounted 
for?     How  high  do  they  rise  there,  and  at  Bristol  in  England  ? 

205.  Define  the  unit  of  altitude.     By  what  circumstances  is 
the  unit  of  altitude  affected  ?     How  is  it  ascertained  ?     State 
it  for  several  places. 


TIDES.  165 

rises  to  a  very  unusual  height.  We  subjoin  from  the 
American  Almanac  a  few  examples  of  the  unit  of  alti- 
tude for  different  places. 

Feet. 

Cumberland,  head  of  the  Bay  of  Fundy,  71 
Boston,  11J 

New  Haven,  8 

New  York,  5 

Charleston,  S.  C.,  6 

206.  The  Establishment  of  any  port  is  the  mean  in- 
terval between  noon  and  the  time  of  high  water,  on  the 
day  of  new  or  full  moon.     As  the  interval  for  any  given 
place  is  always  nearly  the  same,  it  becomes  a  criterion 
of  the  retardation  of  the  tides  at  that  platfe.     On  ac- 
count of  the  importance  to  navigation  of  a  correct 
knowledge  of  the  tides,  the  British  Board  of  Admiralty, 
at  the  suggestion  of  the  Royal  Society,  recently  issued 
orders  to  their  agents  in  various  important  naval  stations, 
to  have  accurate  observations  made  on  the  tides,  with 
the  view  of  ascertaining  the  establishment  and  various 
other  particulars  respecting  each  station  ;  and  the  gov- 
ernment of  the  United  States  is  prosecuting  similar  in- 
vestigations respecting  our  own  ports. 

207.  According  to  Professor  Whewell,  the   tides  on 
the  coast  of  North  America  are  derived  from  the  great 
tide-wave  of  the  South  Atlantic,  which  runs  steadily 
northward  along  the  coast  to  the  mouth  of  the  Bay  of 
Fundy,  where  it  meets  the  northern  tide-wave  flowing 
in  the  opposite  direction.     Hence  he  accounts  for  the 
high  tides  of  the  Bay  of  Fundy. 

208.  The  largest  lakes  and  inland  seas  have  no  per- 
ceptible tides.     This  is  asserted  by  all  writers  respect- 


206.  What,  is  the  establishment,  of  a  port  ?     What  efforts 
have  been  made  to  obtain  accurate  observations  on  the  tides  ? 


166  THE  MOON. 

ing  the  Caspian  and  Euxine,  and  the  same  is  found  to 
be  true  of  the  largest  of  the  North  American  lakes, 
Lake  Superior. 

Although  these  several  tracts  of  water  appear  large 
when  taken  by  themselves,  yet  they  occupy  but  smal1 
portions  of  the  surface  of  the  globe,  as  will  appear  e\ 
ident  from  the  delineation  of  them  on  an  artificial  globe. 
Now  we  must  recollect  that  the  primitive  tides  are  pror 
duced  by  the  unequal  action  of  the  sun  and  moon  upon 
the  different  parts  of  the  earth  ;  and  that  it  is  only  at 
points  whose  distance  from  each  other  bears  a  consider- 
able ratio  to  the  whole  distance  of  the  sun  or  the  moon, 
that  the  inequality  of  action  becomes  manifest.  The 
space  required  is  larger  than  either  of  these  tracts  of 
water.  It  is  obvious  also  that  they  have  no  opportunity 
to  be  subject  to  a  derivative  tide. 

209.  To  apply  the  theory  of  universal  gravitation  to 
all  the  varying  circumstances  that  influence  the  tides, 
becomes  a  matter  of  such  intricacy,  that  La  Place  pro- 
nounces "  the  problem  of  the   tides"  the   most  difficult 
problem  of  celestial  mechanics. 

210.  The  Atmosphere  that  envelops  the  earth,  must 
evidently  be  subject  to  the  action  of  the  same  forces  as 
the  covering  of  waters,  and  hence  we  might  expect  a 
rise  and  fall  of  the  barometer,  indicating  an  atmospheric 
tide  corresponding  to  the  tide  of  the  ocean.     La  Place 
has  calculated  the  amount  of  this  aerial  tide.     It  is  too 
inconsiderable  to  be  detected  by  changes  in  the  barom- 
eter, unless  by  the  most  refined  observations.     Hence  it 
is  concluded,  that  the  fluctuations  produced  by  this  cause 
are  too  slight  to  affect  meteorological  phenomena  in  any 
appreciable  degree. 


207.  How  are  the  tides  on  the  coast  of  North  America  de- 
rived ? 

208.  Why  have  lakes  and  seas  no  tides  ? 

209.  What  is  said  of  the  difficulty  of  applying  the  principle 
of  universal  gravitation  to  all  the  circumstances  of  the  tides  ? 


167 


CHAPTER 


OF  THE  PLANETS  -  THE  INFERIOR  PLANETS,  MERCURY 

AND  VENUS. 

211.  THE  name  planet  signifies  a  wanderer*  and  is 
applied  to  this  class  of  bodies  because  they  shift  their 
positions  in  the  heavens,  whereas  the  fixed  stars  con- 
stantly maintain  the  same  places  with  respect  to  each 
other.  The  planets  known  from  a  high  antiquity,  are 
Mercury,  Venus,  Earth,  Mars,  Jupiter,  and  Saturn.  To 
these,  in  1781,  was  added  Uranus,f  (or  Herschel,as  it  4s 
sometimes  called  from  the  name  of  its  discoverer,)  and, 
as  late  as  the  commencement  of  the  present  century, 
four  more  were  added,  namely,  Ceres,  Pallas,  Juno,  and 
Vesta.  These  bodies  are  designated  by  the  following 
characters  : 

1.  Mercury  $  7.  Ceres  ? 

2.  Venus  $  8.  Pallas  $ 

3.  Earth  -0  9.  Jupiter  U 

4.  Mars  $  10.  Saturn  T? 

5.  Vesta  fi  11.  Uranus  *& 

6.  Juno  § 

The  foregoing  are  called  the  primary  planets.  Sev- 
eral of  these  have  one  or  more  attendants,  or  satellites, 


210.  Has  the  atmosphere  any  tide  ?     Is  it  sufficient  to  influ- 
ence meteorological  phenomena  1 

211.  Whence  is  the  name  planet  derived  ?     Which  of  the 
planets  have  been  long  known  ?     Which  have  been  added  in 
modern  times  ?     Mark  on  paper  or  on  the  black  board,  the 
several  characters  by  which  the  planets  are  designated.     Dis- 
tinguish between  the  primary  and  the  secondary  planets.  What 
bodies  have  satellites  ?     State  the  whole  number  of  planets. 

»  From  the  Greek  n\avnrr,i.  t  From 


168  THE  PLANETS. 

which  revolve  around  them,  as  they  revolve  around  the 
sun.  The  earth  has  one  satellite,  namely,  the  moon  ; 
Jupiter  has  four  ;  Saturn,  seven  ;  and  Uranus,  six.  These 
bodies  also  are  planets,  but  in  distinction  from  the  others 
they  are  called  secondary  planets.  Hence,  the  whole 
number  of  planets  are  29;  viz.  11  primary,  and  IS  sec 
ondary  planets. 

212.  With  the  exception  of  the  four  new  planets, 
'ihese  bodies  have  their  orbits  very  nearly  in  the  same 
plane,  and  are  never  seen  far  from  the  ecliptic.  Mer- 
cury, whose  orbit  is  most  inclined  of  all,  never  departs 
farther  from  the  ecliptic  than  about  7°,  while  most  of 
the  other  planets  pursue  very  nearly  the  same  path  with 
the  earth,  in  their  annual  revolutions  around  the  sun. 
The  new  planets,  hpwever,  make  wider  excursions  from 
the  plane  of  the  ecliptic,  amounting,  in  the  case  of  Pal- 
las, to 


213.  Mercury  and  Venus  are  called  inferior  planets, 
because  they  have  their  orbits  nearer  to  the  sun  than 
that  of  the  earth  ;  while  all  the  others,  being  more  dis- 
tant from  the  sun  than  tfrB  earth,  are  called  superior 
planets.  The  planets  present  great  diversity  among 
themselves  in  respect  to  distance  from  the  sun,  magni- 
tude, time  of  revolution,  and  density.  They  differ  also 
in  regard  to  •satellites,  of  which,  as  we  have  seen,  three 
have  respectively  four,  six,  and  seven,  while  more  than 
half  have  none  at  all.  It  will  aid  the  memory,  and 
render  our  view  of  the  planetary  system  more  clear  and 
comprehensive,  if  we  classify,  as  far  as  possible,  the  x 
various  particulars  comprehended  under  the  foregoing 
heads. 


212.  Near  what  great  circle  are  the  orbits  of  all  the  planets  ? 
How  far  does  Pallas  deviate  from  the  ecliptic  ? 

213.  Why  are  Mercury  and  Venus  called  Inferior  planets  ? 
Why  are  the  other  planets  called  superior  ?     What  diversities 
do  the  planets  exhibit  among  themselves  ? 


DISTANCES  FROM  THE  SUN.  169 


214.    DISTANCES  FROM  THE  SUN. 

1.  Mercury,  .  .  37,000,000 

2.  Venus,  .  .  68,000,000 

3.  Earth,  .  .  95,000,000 

4.  Mars,  .  .  142,000,000 

5.  Vesta,          _    .  .  225,000,000 

6.  Juno,  .  .  ) 

7.  Ceres,  .  .  V  261,000,000 
S.Pallas,  .  .  ) 

9.  Jupiter,  .  .  485,000,000 

10.  Saturn,  .  .  890,000,000 

11.  Uranus,  .  1800,000,000 

The  dimensions  of  the  planetary  system  are  seen 
from  this  table  to  be  vast,  comprehending  a  circular 
space  thirty  six  hundred  millions  of  miles  in  diameter. 
A  railway  car,  travelling  constantly  at  the  rate  of  20 
miles  an  hour,  would  require  more  than  20,000  years  to 
cross  the  orbit  of  Uranus. 

It  may  aid  the  memory  to  remark,  that  in  regard  to 
the  planets  nearest  the  sun,  the  distances  increase  in  an 
arithmetical  ratio,  while  those  most  remote,  increase  in 
a  geometrical  ratio.  Thus,  if  we  add  30  to  the  distance 
of  Mercury,  it  gives  us  nearly  that  of  Venus  ;  30  more 
gives  that  of  the  Earth  ;  while  Saturn  is  nearly  twice 
the  distance  of  Jupiter,  and  Uranus  twice  the  distance 
of  Saturn.  Between  the  orbits  of  Mars  and  Jupiter,  a 
great  chasm  appeared,  which  broke  the  continuity  of  the 
series  ;  but  the  discovery  of  the  new  planets  has  filled 
the  void. 


214.  State  the  distance  of  each  of  the  planets  from  the  sun. 
What  is  said  of  the  dimensions  of  the  planetary  system  ?  How 
do  the  distances  of  those  planets  which  are  nearest  the  sun  in- 
crease 1  Also  those  which  are  more  distant  ?  How  may  the 
mean  distances  of  the  planets  from  the  sun  be  determined  ? 
Give  an  example  in  computing  the  distance  of  Jupiter. 

15 


170  THE  PLANETS. 

The  mean  distances  of  the  planets  from  the  sun,  may 
be  determined  by  means  of  Kepler's  law,  that  the  squares 
of  the  periodical  times  are  as  the  cubes  of  the  distances. 
Thus  the  earth's  distance  being  previously  ascertained 
by  means  of  the  sun's  horizontal  parallax,  and  the  pe- 
riod of  any  other  planet,  as  Jupiter,  being  learned  from 
observation,  we  say  as  3G5.2562  :  43S2.5852*  :  :  I3  : 
5.2023,  which  equals  the  cube  of  Jupiter's  distance  from 
the  sun,  and  its  root  equals  that  distance  itself. 
/ 

215.    MAGNITUDES. 

Diam.  in  Miles.    Mean  apparent  Diam.    Volume. 

Mercury,  ;£.  .  .  3140  6".9  TV 

Venus,  .  .  '•_.„•  7700  61".9  ^ 

Earth,  .  .  .  7912  1 

Mars,  .  .  .  4200  6".3  T 

Ceres,  .  .  .  160  0".5 

Jupiter,  .  .  .  89000  36".7  1281 

Saturn,  .  .  .  79000  16".2  995 

Uranus,  .  .  .  35000  4".0  80 

We  remark  here  a  great  diversity  in  regard  4o  magni- 
tude, a  diversity  which  does  not  appear  to  be  subject  to 
any  definite  law.  While  Venus,  an  inferior  planet,  is 
f§  as  large  as  the  earth,  Mars,  a  superior  planet  is  only  y, 
while  Jupiter  is  1281  times  as  large.  Although  several 
of  the  planets,  when  nearest  to  us,  appear  brilliant  and 
large  when  compared  with  the  fixed  stars,  yet  the  angle 
which  they  subtend  is  very  small,  that  of  Venus,  the 
greatest  of  all,  never  exceeding  about  1',  or  more  exactly 
61  ".9,  and  that  of  Jupiter  being  when  greatest  only 
about  f  of  a  minute. 


215.  State  the  diameter  of  each  of  the  planets.  -What  diver- 
sities occur  in  regard  to  their  magnitudes  ?  How  great  angles 
do  Venus  and  Jupiter  subtend  ? 


*  This  is  the  number  of  days  in  one  revolution  of  Jupiter. 


PERIODIC  TIMES — MERCURY  AND    VENUS.  171 

216.    PERIODIC  TIMES. 

Revolution  in  its  orbit.  Mean  daily  motion. 

Mercury,      3  months,  or        88  days,  4°     5'  32  '.6 

Venus,          7|       «  "       224  «  1°  36'    7".8 

Earth,            1  year,  "       365  "  0°  59'     8".3 

Mars,            2  years,  "       687  "  0°  31'  26".7 

Ceres,           4     "  "1681  «  0°  12'  50".9 

Jupiter,  12     «  "     4332  "  0°     4'  59".3 

Saturn,  29     «  "  10759  "  0°     2'     0".6 

Uranus,  84     "  "  30686  "  0°     0'  42".4 

From  this  view,  it  appears  that  the  planets  nearest  the 
sun  move  most  rapidly.  Thus  Mercury  performs  nearly 
350  revolutions  while  Uranus  performs  one.  This  is 
evidently  not  owing  merely  to  the  greater  dimensions  of 
the  orbit  of  Uranus,  for  the  length  of  its  orbit  is  not  50 
times  that  of  the  orbit  of  Mercury,  while  the  time  em- 
ployed in  describing  it  is  350  times  that  of  Mercury. 
Indeed  this  ought  to  follow  from  Kepler's  law  that  the 
squares  of  the  periodical  times  are  as  the  cubes  of  the 
distances,  from  which  it  is  manifest  that  the  times  of 
revolution  increase  fasten  than  the  dimensions  of  the  or- 
bit. Accordingly,  the  apparent  progress  of  the  most 
distant  planets  is  exceedingly  slow,  the  daily  rate,  of 
Uranus  being  only  42'',4  per  day  ;  so  that  for  weeks  and 
months,  and  even  years,  this  planet  but  slightly  changes 
its  place  among  the  stars. 

THE  INFERIOR  PLANETS,  MERCURY  AND  VENUS. 

217.  The  inferior  planets,  Mercury  and  Venus,  hav- 
ing their  orbits  so  far  within  that  of  the  earth,  appear  to 
us  as  attendants  upon  the  sun.  Mercury  never  appears 
farther  from  the  sun  than  29°  (28°  48')  and  seldom  so 


216.  State  the  periodic  time  of  each  of  the  planets.  Which 
planets  move  most  rapidly  ?  How  many  revolutions  does  Mer- 
cury perform  while  Uranus  performs  one  ?  What  is  the  daily 
rate  of  Uranus  ? 


172 


THE  PLANETS. 


far ;  and  Venus  never  more  than  about  47°  (4T  12'). 
Both  planets,  therefore,  appear  either  in  the  west  soon 
after  sunset,  or  in  the  east  a  little  before  sunrise.  In 
high  latitudes,  where  the  twilight  is  prolonged,  Mercury 


can  seldom  be  seen  with  the  naked  eye,  and  then  only 
at  the  periods  of 'its  greatest  elongation.*  The  reason 
of  this  will  readily  appear  from  the  following  diagram. 

Fig.  40. 


Let  S  (Fig.  40,)  represent  the  sun,  ADB  the  orbit  of 
Mercury,  and  E  the  place  of  the  Earth.  Each  of  the 
planets  is  seen  at  its  greatest  elongation,  when  a  line, 
EA  or  EB  in  the  figure,  is  a  tangent  to  its  orbit.  Then 
the  sun  being  at  S'  in  the  heavens,  the  planet  will  be 


217.  What  is  Mercury's  greatest  elongation  from  the  sun  ? 
What  is  Venus's  ?  What  is  said  respecting  the  difficulty  of  see- 
ing Mercury  ?  Explain  by  figure  40. 


*  Copernicus  is  said  to  have  lamented  on  his  death-bed  that  he  had 
never  been  able  to  obtain  a  sight  of  Mercury,  and  Delambre  saw  it  but 
twice. 


MERCURY  AND  VENUS.  173 

seen  at  A'  and  B',  when  at  its  greatest  elongations,  and 
will  appear  no  further  from  the  sun  than  the  arc  S'A'  or 
S'B'  respectively. 

218.  A  planet  is  said  to  be  in  Conjunction  with  the 
sun,  when  it  is  seen  in  the  same  part  of  the  heavens 
with  the  sun,  or  when  it  has  the  same  longitude.     Mer- 
cury and  Venus  have  each  two  conjunctions,  the  inferior, 
and  the  superior.     The  inferior  conjunction  is  its  posi- 
tion when  in  conjunction  on  the  same   side  of  the  sun 
with  the  earth,  as  at  C  in  the  figure  :  the  superior  con- 
junction is  its  position  when  on  the  side  of  the  sun  most 
distant  from  the  earth,  as  at  D. 

219.  The  period  occupied  by  a  planet  between  two 
successive  conjunctions  with  the  earth,  is  called  its  sy- 
nodical  revolution.     Both  the  planet  and  the  earth  being 
in  motion,  the  time  of  the  synodical  revolution  exceeds 
that  of  the  sidereal  revolution  of  Mercury  or  Venus ; 
for  when  the   planet  comes  round  to  the  place  where  it 
before  overtook  the  earth,  it  does  not  find  the  earth  at 
that  point,  but  far  in  advance  of  it-     Thus,  let  Mercury 
come  into  inferior  conjunction  with  the  earth  at  C,  (Fig. 
40.)     In  about  88  days,  the  planet  will  come  round  to 
the  same  point  again;    but  meanwhile  the  earth  has 
moved  forward  through  the  arc  EE',  and  will  continue 
to  move  while  the  planet  is  moving  more  rapidly  to  over- 
take her,  the  case  being  analogous  to  that  of  the  hour 
and  minute  hand  of  a  clock. 

The  synodical  period  of  Mercury  is  1 16,  and  of  Venus 
584  days. 


218.  When  is  a  planet  said  to  be  in  conjunction  with  the 
sun  ?     What  conjunctions  have  the  inferior  planets  ? 

219.  Define  the  synodical  revolution.    How  does  this  period 
compare  with  the  sidereal  revolution  ?     Explain  by  figure  40. 
What  is  the  synodical  period  of  Mercury  and  Venus  respect* 
ively  ? 

15* 


174  THE    PLANETS. 

( 

220.  The  motion  of  an   inferior  planet  is  direct  in 
passing  through  its  superior  conjunction,  and  retrogade 
in  passing  through  its  inferior  conjunction.     Thus  Ve- 
nus, while  going  from  B  through  D  to  A,  (Fig.  40,) 
moves  in  the  order  of  the  signs,  or  from  west  to  east, 
and  would  appear  to  traverse  the  celestial  vault  B'S'A' 
from  right  to  left ;  but  in  passing  from  A  through  C  to 
B,  her  course  would  be  retrogade,  returning  on  the  same 
arc  from  left  to  right.     If  the  earth  were  at  rest,  there- 
fore, (and  the  sun,  of  course,  at  rest,)  the  inferior  planets 
would  appear  to  oscillate  backwards  and  forwards  across 
the  sun.     But,  it  must  be  recollected,  that  the  earth  is 
moving  in  the  same  direction  with  the  planet,  as  respects 
the  signs,  but  with  a  slower  motion.     This  modifies  the 
motions  of  the  planet,  accelerating  it  in  the  superior  and 
retarding  it  in  the  inferior  conjunctions.     Thus  in  figure 
40,  Venus  while  moving  through  BDA  would  seem  to 
move  in  the  heavens  from  B'  to  A7  were  the  earth  at 
rest ;  but  meanwhile  the  earth  changes  its  position  from 
E  to  E'  by  which  means  the  planet  is  not  seen  at  A' 
but  at  A",  being  accelerated  by  the  arc  A' A"  in  conse- 
quence of  the  earth's  motion.     On  the  other  hand,  when 
the  planet  is  passing  through  its  inferior  conjunction 
ACB,  it  appears  to  move  backwards  in  the  heavens  from 
A'  to  B'  if  the  earth  is  at  rest,  but  from  A'  to  B"  if  the 
earth  has  in  the  mean  time  moved  from  E  to  E'  being 
retarded  by  the  arc  B'B".     Although  the  motions  of  the 
earth  have  the  effect  to  accelerate  the  planet  in  the  superi- 
or conjunction,  and  to  retard  it  in  the  inferior,  yet,  on  ac- 
count of  the  greater  distance,  the  apparent  motion  of  the 
planet  is  much  slower  in  the  superior  than  in  the  infe- 
rior conjunction. 

221.  When  passing  from  the  superior  to  the  inferior 
conjunction,  or  from  the  inferior  to  the  superior  conjunc- 


220.  When  is  the  motion  of  an  inferior  planet  direct  and 
when  retrograde  ?  Explain  by  figure  40.  If  the  earth  were  at 
rest,  how  would  the  inferior  planets  appear  to  move  ?  Show 
how  the  earth's  motion  modifies  the  apparent  motions. 


MERCURY  AND  VENUS.  175 

tion  through  the  greatest  elongations,  the  inferior  plan- 
ets are  stationary. 

If  the  earth  were  at  rest,  the  stationary  points  would 
be  at  the  greatest  elongations  as  at  A  and  B,  for  then  the 
planet  would  be  moving  directly  towards  or  from  the 
earth,  and  would  be  seen  for  some  time  in  the  same 
place  in  the  heavens ;  but  the  earth  itself  is  moving 
nearly  at  right  angles  to  the  line  of  the  planet's  motion, 
that  is,  the  line  which  is  drawn  from  the  earth  to  the 
planet  through  the  point  of  greatest  elongation  ;  hence  a 
direct  motion  is  given  to  the  planet  by  this  cause.  When 
the  planet,  however,  has  passed  this  line  by  its  superior 
velocity,  it  soon  overcomes  this  tendency  of  the  earth  to 
give  it  a  relative  motion  eastward,  and  becomes  retro- 
grade as  it  approaches  the  inferior  conjunction.  Its  sta- 
tionary point  obviously  lies  between  its  place  of  greatest 
elongation,  and  the  place  where  its  motion  becomes  re- 
trograde. Mercury  is  stationary  at  an  elongation  of 
from  15°  to  20°  from  the  sun  ;  and  Venus  at  about  29°. 

222.  Mercury  and  Venus  exhibit  to  the  telescope,  pha- 
ses similar  to  those  of  the  moon. 

When  on  the  side  of  their  inferior  conjunction,  these 
planets  appear  horned,  like  the  moon  in  her  first  and  last 
quarters  ;  and  whqn  on  the  side  of  their  superior  con- 
junctions they  appear  gibbous.  At  the  moment  of  su- 
perior conjunction,  the  whole  enlightened  orb  of  the 
planet  is  turned  towards  the  earth,  and  the  appearance 
would  be  that  of  the  full  moon,  but  the  planet  is  too 
near  the  sun  to  be  commonly  visible. 

These  different  phases  show  these  bodies  are  opake, 
and  shine  only  as  they  reflect  to  us  the  light  of  the  sun ; 
and  the  same  remark  applies  to  all  the  planets. 


221.  When  are  the  inferior  planets  stationary  ?     Why  are 
they  not  stationary  at  the  points  of  greatest  elongation  ?  At  what 
elongation  are  Mercury  and  Venus  stationary  respectively  ? 

222.  What  phases  do  Mercury  and  Venus  exhibit  ?  Explain 
by  figure  40,     Whence  do  these  bodies  derive  their  light  ?    Is 
the  same  true  of  the  other  planets  ? 


176  THE  PLANETS. 

223.  The  orbit  of  Mercury  is  the  most  eccentric,  and 
the  most  inclined  of  all  the  planets  ;*  while  that  ofi  Ve- 
nus varies  but  little  from  a  circle,  and  lies  much  nearer 
to  the  ecliptic. 

The  eccentricity  of  the  orbit  of  Mercury  is  nearly  £ 
its  semi-major  axis,  while  that  of  Venus  is  only  y^  ; 
the  inclination  of  Mercury's  orbit  is  7°,  while  that  of 
Venus  is  less  than  3J°.  Mercury,  on  account  of  his  dif- 
ferent distances  from  the  earth,  varies  much  in  his  appa- 
rent diameter,  which  is  only  5"  in  the  apogee,  but  12" 
in  the  perigee.  The  inclination  of  his  orbit  to  his  equa- 
tor being  very  great,  the  changes  of  his  seasons  must  be 
proportionally  great. 

These  different  aspects  of  an  inferior  planet  will  be 
easily  understood  from  Fig.  41,  where  the  earth  is  at  E, 

Fig.  41. 


and  the  planet  is  represented  in  various  positions  in  its 
revolutions  around  the  sun.  When  at  A,  in  the  supe- 
rior conjunction,  the  whole  enlightened  disk  is  turned 
towards  us  ;  at  D,  in  the  inferior  conjunction,  the  en- 
lightened side  is  turned  entirely  from  us  ;  and  at  the 
quadratures  B  and  C,  half  the  disk  is  in  view.  Between 
A  and  B,  and  A  and  C,  the  planet  is  gibbous,  like  the 
moon  in  her  second  and  third  quarters  ;  and  between  B 


223.  What  is  said  of  the  eccentricity  and  inclination  of  the 
orbit  of  Mercury  ?  How  does  the  apparent  diameter  of  Mer 
cury  vary  ?  How  are  his  changes  of  seasons  ? 

*  The  new  planets  of  course  excepted 


MERCURY  AND  VENUS.  177 

?wid  D,  and  C  and  D,  the  planet  is  horned,  like  the  moon 
in  her  first  and  last  quarters. 

224.  An  inferior  planet  is  brightest  at  a  certain  point 
between  its  greatest  elongation  and  inferior  conjunction. 

Its  maximum  brilliancy  would  happen  at  the  inferior 
conjunction,  (being  then  nearest  to  us,)  if  it  shined  by 
its  own  light ;  but  in  that  position  its  dark  side  is  turned 
towards  us.  Still,  its  maximum  cannot  be  when. most 
of  the  illuminated  side  is  towards  us ;  for  then,  being  at 
the  superior  conjunction,  it  is  at  its  greatest  distance 
from  us.  The  maximum  must  therefore  be  somewhere 
between  the  two.  Venus  gives  her  greatest  light  when 
about  40°  from  the  sun. 

225.  Mercury  and   Venus    oik  revolve  on  their  axes, 
in  nearly  the  same  time  with  the  earth. 

The  diurnal  period  of  Mercury  is  24h.  5m.  28s.,  and 
that  of  Venus  23h.  21m.  7s.  The  revolutions  on  their 
axes  have  been  determined  by  means  of  some  spot  or 
mark  seen  by  the  telescope,  as  the  revolution  of  the  sun 
on  his  axis  is  ascertained  by  means  of  his  spots. 

226.  Venus  is  regarded  as  the  most  beautiful  of  the 
planets,  and  is  well  known  as  the  morning  and  evening 
star.     The  most  ancient  nations  did  not  indeed  recog- 
nize the  evening  and  morning  star  as  one  and  the  same 
body,  but  supposed  they  were  different  planets,  and  ac- 
cordingly gave  them  different  names,  calling  the  morn- 
ing star  Lucifer,  and  the  evening  star  Hesperus.     At  her 
period  of  greatest  splendor,  Venus  casts  a  shadow,  and  is 
sometimes  visible  in  broad  daylight.     Her  light  is  then 
estimated  as  equal  to  that  of  twenty  stars  of  the  first 


224.  When  is  an  inferior  planet  brightest  1     Why  not  when 
nearest  to  us  1  Why  not  when  most  of  the  illuminated  side  is 
turned  towards  us  1 

225.  In  what  time  do  Mercury  and  Yenus,  respectively,  re- 
volve on  their  axes  1     How  are  these  periods  ascertained  1 


178  THE  PLANETS. 

magnitude.  At  her  period  of  greatest  elongation,  Ve- 
nus is  visible  from  three  to  four  hours  after  the  setting 
or  before  the  rising  of  the  sun. 

227.  Every  eight  years,  Venus  forms  her  conjunctions 
with  the  sun  in  the  same  part  of  the  heavens. 

For,  since  the  synodical  period  of  Venus  is  584  days, 
and  her  sidereal  period  224.7, 

224.7  :  360°: :  584  :  935.6=the  arc  of  longitude  de- 
scribed by  Venus  between  the  first  and  second  conjunc- 
tions. Deducting  720°,  or  two  entire  circumferences, 
the  remainder,  21  #.6,  shows  how  far  the  place  of  the 
second  conjunction  is  in  advance  of  the  first.  Hence, 
in  five  synodical  revolutions,  or  2920  days,  the  same 
point  must  have  advanced  215°.6x  5  =  1078°,  which  is 
nearly  three  entire  circumferences,  so  that  at  the  end  of 
five  synodical  revolutions,  occupying  2920  days,  or  8 
years,  the  conjunction  of  Venus  takes  place  nearly  in 
the  same  place  in  the  heavens  as  at  first. 

Whatever  appearances  of  this  planet,  therefore,  arise 
from  its  position  with  respect  to  the  earth  and  the  sun, 
they  are  repeated  every  eight  years  in  nearly  the  same 
form. 

TRANSITS  OF  THE  INFERIOR  PLANETS. 

228.  The  Transit  of  Mercury  or  Venus,  is  its  passage 
across  the  sun's  disk,  as  the  moon  passes  over  it  in  a  solar 
eclipse. 

As  a  transit  takes  place  only  when  the  planet  is  in 
inferior  conjunction,  at  which  time  her  motion  is  retro- 
grade, it  is  always  from  left  to  right,  and  the  planet  is 
seen  projected  on  the  solar  disk  in  a  black  round  spot. 


226.  What  erroneous  notions  had  the  ancients  respecting  the 
morning  and  evening  star  ?     What  is  said  of  the  brilliancy  ot 
Venus  at  her  greatest  splendor  ?     How  long  may  Venus  be  in 
sight  after  sunset  ? 

227.  What  happens  to  Venus  every  eight  years  ? 


MERCURY  AND  VENUS. 


Were  the  orbits  of  the  inferior  planets  coincident  with 
the  plane  of  the  earth's  orbit,  a  transit  would  occur  to 
some  part  of  the  earth  at  every  inferior  conjunction. 
But  the  orbit  of  Venus  makes  an  angle  of  3^°  with  the 
ecliptic,  ana  Mercury  an  angle  of  7°  ;  and,  moreover, 
the  apparent  diameter  of  each  of  these  bodies  is  very 
small,  both  of  which  circumstances  conspire  to  render  a 
transit  a  comparatively  rare  occurrence,  since  it  can  hap- 
pen only  when  the  sun,  at  the  time  of  an  inferior  con- 
junction, chances  to  be  at  or  extremely  near  the  planet's 
node.  The  nodes  of  Mercury  lie  in  longitude  46°  and 
226°,  points  which  the  sun  passes  through  in  May  and 
November.  It  is  only  in  these  months,  therefore,  that 
transits  of  Mercury  can  occur.  For  a  similar  reason, 
those  of  Venus  occur  only  in  June  and  December.  Since, 
however,  the  nodes  of  both  planets  have  a  small  retro- 
grade motion,  the  months  in  which  transits  occur  will 
change  in  the  course  of  ages 

229.  Transits  of  Mercury  occur  more  frequently  than 
those  of  Venus.  The  periodic  times  of  Mercury  and 
the  earth  are  so  adjusted  to  each  other,  that  Mercury 
performs  nearly  29  revolutions  while  the  earth  performs 
7.  If,  therefore,  the  two  bodies  meet  at  the  node  in  any 
given  year,  seven  years  afterwards  they  will  meet  nearly 
at  the  same  node,  and  a  transit  may  take  place,  accord- 
ingly, at  intervals  of  7  years.  But  54  revolutions  of 
Mercury  correspond  still  nearer  to  13  revolutions  of  the 


228.  What  is  meant  by  the  transit  of  Mercury  or  Venus  ? 
When  only  can  a  transit  take  place  ?  What  angles  do  the  or- 
bits of  Venus  and  Mercury  respectively  make  with  the  ecliptic  ? 
In  what  months  does  the  sun  pass  through  the  nodes  of  each 
of  these  planets  ? 

229.  Which  planet  has  the  most  frequent-transits  ?    What  is 
the  shortest  interval  of  the  transits  of  Mercury  ?    What  are  the 
longer  intervals  ?     When  will  the  next  occur  ?     What  are  in- 
tervals of  the  transits  of  Venus  ?     When  was  the  last  transit 
of  Venus,  and  when  will  the  next  occur  ? 


380  THE  PLANETS. 

earth,  and  therefore  a  transit  is  still  more  probable  after 
intervals  of  13  years.  At  intervals  of  33  years,  transits 
of  Mercury  are  exceedingly  probable,  because  in  that 
time  Mercury  makes  almost  exactly  137  revolutions. 
Intermediate  transits  however  may  occur  at  the  other 
node,  these  intervals  having  reference  merely  to  the 
same  node.  Thus  transits  of  Mercury  happened  at  the 
ascending  node  in  1815,  and  1822,  at  intervals  of 
7  years ;  and  at  the  descending  node  in  1832,  which 
will  return  in  1845,  after  an  interval  of  13  years.  Tran- 
sits of  Venus  arte  much  more  unfrequent  than  those  of 
Mercury,  Eight  revolutions  of  the  earth  are  completed 
in  nearly  the  same  time  as  thirteen  revolutions  of  Venus, 
and  hence  two  transits  of  Venus  may  occur  at  an  in- 
terval of  8  years,  as  was  the  case  at  the  last  return  of 
this  phenomenon,  one  transit  having  occurred  in  1761, 
and  another  in  1769.  But  if  a  transit  does  not  happen 
after  8  years,  it  will  not  happen,  at  the  same  node,  until 
an  interval  of  235  years ;  but  intermediate  transits  may 
occur  at  the  other  node.  The  next  transit  of  Venus  will 
take  place  in  1874,  being  235  years  after  the  first  that  was 
ever  observed,  which  occurred  in  the  year  1639.  In  the 
mean  time,  as  already  mentioned,  two  transits  have  oc- 
curred at  the  other  node,  at  intervals  of  8  years. 

230.  The  great  interest  attached  by  astronomers  to  a 
transit  of  Venus,  arises  from  its  furnishing  the  most  accu- 
rate means  in  our  power  of  determining  the  sun's  hori- 
zontal parallax — an  element  of  great  importance,  since  it 
leads  us  to  a  knowledge  of  the  distance  of  the  earth  from 
the  sun,  and,  consequently,  by  the  application  of  Kepler's 
«aw,  (Art.  130,)  of  the  distances  of  all  the  other  planets. 
Hence,  in  1769,  great  efforts  were  made  throughout  the 
civilized  world,  under  the  patronage  of  different  govern- 


230.  Why  is  so  much  interest  attached  to  the  transits  ol 
Venus  ?  What  efforts  were  made  to  observe  it  in  1769  ?  Why 
cannot  we  ascertain  the  horizontal  parallax  of  the  sun  in  the 
same  way  as  we  do  that  of  the  moon  ? 


MERCURY  AND  VENUS.  181 

ments,  to  observe  this  phenomenon  under  circumstances 
the  most  favorable  for  determining  the  parallax  of  the 
sun. 

The  common  methods  of  finding  the  parallax  of  a 
heavenly  body  cannot  be  relied  on  to  a  greater  degree 
of  accuracy  than  4".  In  the  case  of  the  moon,  whose 
greatest  parallax  amounts  to  about  1°,  this  deviation 
from  absolute  accuracy  is  not  material ;  but  it  amounts 
to  nearly  half  the  entire  parallax  of  the  sun. 

231.  If  the  sun  and  Venus  were  equally  distant  from 
us,  they  would  be  equally  affected  by  parallax  as  viewed 
by  spectators  in  different  parts  of  the  earth,  and  hence 
their  relative  situation  would  not  be  altered  by  it ;  but 
since  Venus,  at  the  inferior  conjunction,  is  only  about 
one  third  as  far  off  as  the  sun,  her  parallax  is  propor- 
tionally greater,  and  therefore  spectators  at  distant  points 
will  see  Venus  projected  on  different  parts  of  the  so- 
lar disk,  as  the  planet  traverses  the  disk.  Astron- 
omers avail  themselves  of  this  circumstance  to  ascer- 
tain the  sun's  horizontal  parallax.  In  order  to  make 
the  difference  as  large  as  possible  very  distant  pla- 
ces are  selected  for  observation.  Thus  in  the  transit 
of  1769,  among  the  places  selected,  two  of  the  most 
favorable  were  Wardhuz  in  Lapland,  and  Oteheite,  one 
of  the  South  Sea  Islands. 

The  appearance  of  Venus  on  the  sun's  disk,  being 
that  of  a  well  defined  black  spot,  and  the  exactness  with 
which  the  moment  of  external  or  internal  contact  may 
be  determined,  are,circumstances  favorable  to  the  exact- 
ness of  the  result ;  and  astronomers  repose  so  much  con- 
fidence in  the  estimation  of  the  sun's  horizontal  parallax 
as  derived  from  the  observations  on  the  transit  of  1769, 
that  this  important  element  is  thought  to  be  ascertained 


231.  How  is  Venus  projected  on  the  sun  to  spectators  in 
different  parts  of  the  earth  ?  What  places  were  selected  for 
observing  the  transit  of  1769  ? 

16 


182  THE  PLANETS. 

within  ^  of  a  second.  The  general  result  of  all  these 
observations  gives  the  sun's  horizontal  parallax  8".6,  or 
more  exactly,  8."5776. 

232.  During  the  transits  of  Venus  over  the  sun's  disk 
in  1761  and  1769,  a  sort  of  penumbral  light  was  ob- 
served around  the  planet  by  several  astronomers,  which 
was  thought  to  indicate  an  atmosphere.  This  appear- 
ance was  particularly  observable  while  the  planet  was 
coming  on  and  going  off  the  solar  disk.  The  total  im- 
mersion and  emersion  were  not  instantaneous ;  but  as 
two  drops  of  water  when  about  to  separate,  form  a  liga- 
ment between  them,  so  there  was  a  dark  shade  stretched 
out  between  Venus  and  the  sun,  and  when  the  ligament 
broke,  the  planet  seemed  to  have  got  about  an  eighth  part 
of  her  diameter  from  the  limb  of  the  sun.  The  various 
accounts  of  the  two  transits  abound  with  remarks  like 
these,  which  indicate  the  existence  of  an  atmosphere 
about  Venus  of  nearly  the  density  and  extent  of  the 
earth's  atmosphere.  Similar  proofs  of  the  existence  of 
an  atmosphere  around  this  planet,  are  derived  from  ap- 
pearances of  twilight. 

The  elder  astronomers  imagined  they  had  discovered 
a  satellite  accompanying  Venus  in  her  transit.  If  Venus 
had  in  reality  any  satellite,  the  fact  would  be  obvious  at 
her  transits,  as  the  satellite  would  be  projected  near  the 
primary  on  the  sun's  disk ;  but  later  astronomers  have 
searched  in  vain  for  any  appearances  of  the  kind,  and 
the  inference  is  that  former  astronomers  were  deceived 
by  some  optical  illusion. 

Astronomers  have  detected  very  high  mountains  on 
Venus,  sometimes  reaching  to  the  elevation  of  22  miles  ; 
and  it  is  remarkable  that  the  highest  mountains  in  Ve- 
nus, in  Mercury,  in  the  moon,  and  in  the  earth,  are  al- 
ways in  the  southern  hemisphere. 


232.  What  indications  have  been  observed  of  an  atmos- 
phere about  Venus  ?  Has  Venus  any  Satellite  ?  What  is  said 
of  the  mountains  of  Venus  ? 


SUPERIOR  PLANETS.  183 


CHAPTER    VIII. 

OP  THE  SUPERIOR  PLANETS MARS,  JUPITER,  SATURN,  AND 

URANUS CERES,  PALLAS,  JUNO,  AND  VESTA. 

233.  THE  Superior  planets  are  distinguished  from  the 
Inferior,  by  being  seen  at  all  distances  from  the  sun 
from  0°  to  180°.     Having  tfeeir  orbits  exterior  to  that 
of  the  earth,  they  of  course  never  come  between  us  and 
the  sun,  that  is,  they  never  have  any  inferior  conjunction 
like  Mercury  and  Venus,  but  they  are  sometimes  seen  in 
superior  conjunction,  and  sometimes  in  opposition.     Nor 
do  they,  like  the  inferior  planets,  exhibit  to  the  telescope 
different  phases,  but,  with  a  single  exception,  they  al- 
ways present  the  side  that  is  turned  towards  the  earth 
fully  enlightened.     This  is  owing  to  their  great  distance 
from  the  earth  ;  for  were  the  spectator  to  stand  upon  the 
sun,  he  would  of  course  always  have  the   illuminated 
side  of  each  of  the  planets  turned  towards  him  ;  but, 
so  distant  are  all  the  superior  planets  except  Mars,  that 
they  are  viewed  by  us  very  nearly  in  the  same  manner 
as  they  would  be  if  we  actually  stood  on  the  sun. 

234.  MARS  is  a  small  planet,  his  diameter  being  only 
about  half  of  that  of  the  earth,  or  4200  miles.     He  also, 
at  times,  comes  nearer  to  the  earth  than  any  other  planet 
except  Venus.     His   mean  distance  from   the   sun   is 
142,000,000  miles;  but  his  orbit  is  so  eccentric  that  his 
distance  varies  much  in  different  parts  of  his  revolution. 
Mars  is  always  very  near  the  ecliptic,  never  varying  from 


233.  Name  the   Superior  Planets.     How  are  they  distin- 
guished from  the  Inferior  ?     Whidh  of  them  exhibits  phases  ? 
Why  do  not  the  rest  ? 

234.  Mars. — State  his  diameter — Mean  distance  from  the 
sun — inclination  of  his  orbit.     How  distinguished  from  the 
other  planets  ?     Why  do  his  brightness  and  apparent  magni- 
tude vary  so  much  ?     Illustrate  by  figure  42. 


184 


THE    PLANETS. 


it  2°.  He  is  distinguished  from  all  the  planets  by  his 
deep  red  color,  and  fiery  aspect ;  but  his  brightness  and 
apparent  magnitude  vary  much  at  different  times,  being 
sometimes  nearer  to  us  than  at  others,  by  the  whole  di- 
ameter of  the  earth's  orbit-,  that  is,  by  about  190,000,000 
of  miles.  When  Mars  is  on  the  same  side  of  the  sun 
with  the  earth,  or  at  his  opposition,  he  comes  within 
47,000,000  miles  of  the  earth,  and  rising  about  the  time 
the  sun  sets,  surprises  us  by  his  magnitude  and  splen- 
dor ;  but  when  he  passes  to  the  other  side  of  the  sun  to 
his  superior  conjunction,  he  dwindles  to  the  appearance 
of  a  small  star,  being  then  237,000,000  miles  from  us. 
Thus,  let  M  (Fig.  42,)  represent  Mars  in  opposition, 
and  M'  in  the  superior  conjunction,  while  E  represents 
the  earth.  It  is  obvious  that  in  the  former  situation,  the 
planet  must  be  nearer  to  the  earth  than  in  the  latter 
by  the  whole  diameter  of  the  earth's  orbit. 

Tig.  42. 


235.  Mars  is  the  only  one  of  the  superior  planets 
which  exhibits  phases.  When  he  is  towards  the  quad- 
ratures at  Q  or  Q',  it  is  evident  from  the  figure  that 
only  a  part  of  the  circle  of  illumination  is  turned  towards 


MARS.  185 

the  earth,  such  a  portion  of  the  remoter  part  of  it  being 
concealed  from  our  view  as  to  render  the  form  more  or 
less  gibbous. 

236.  When  viewed  with  a  powerful  telescope,  the 
surface  of  Mars  appears  diversified  with  numerous  vari- 
eties of  light  and  shade.     The  region  around  the  poles 
is  marked  by  white  spots,  which  vary  their  appearance 
with  the  changes  of  seasons  in  the  planets.     Hence  Dr. 
Herschel  conjectured  that  they  were  owing  to  ice  and 
snow,  which  alternately  accumulates  and  melts,  accord- 
ing to  the  position  of  each  pole  with  respect  to  the  sun. 
It  has  been  cpmmon  ta  ascribe  the  ruddy  light  of  this 
planet  to  an  extensive  and  dense  atmosphere,  which  was 
said  to  be  distinctly  indicated,  by  the  gradual  diminution 
of  light  observed  in  a  star  as  it  approached  very  near  to 
the  planet  in  undergoing  an  occultation ;  but  more  re- 
cent observations  afford  no  such  evidence  of  an  atmos- 
phere. 

237.  By  observations  on  the  spots,  we  learn  that  Mars 
revolves  on  his  axis  in  very  nearly  the  same  time  with 
the  earth,  (24h.  39m.  21s.3) ;  and  that  the  inclination  of 
his  axis  to  that  of  his  orbit  is  also  nearly  the  same, 
being  30°  18'  10".8. 

As  the  diurnal  rotation  of  Mars  is  nearly  the  same  as 
that  of  the  earth,  we  might  expect  a  similar  flattening  at 
the  poles,  giving  to  the  planet  a  spheroidal  figure.  In- 
deed the  compression  or  ellipticity  of  Mars  greatly  ex- 
ceeds that  of  the  earth,  being  no  less  than  14  of  the 
equatorial  diameter,  while  that  of  the  earth  is  only 


235.  Show  why  Mars  should  exhibit  phases. 

236.  How  is  the  surface  of  Mars  diversified  ?  What  is  seen 
around  the   poles  ?     What  indications  are  there   of  ice  and 
snow  ?     To  what  is  the  ruddy  hue  of  Mars  ascribed  ? 

237.  How  do  we  learn  his  revolution  on  his  axis  ?     In  what 
time  does  it  take  place  ?     What  is  the  figure  of  Mars  ?     How 
does  its  ellipticity  compare  with  that  of  the  earth  ? 

16* 


186 


THE  PLANETS. 


This  remarkable  flattening  of  the  poles  of  Mars  has  been 
supposed  to  arise  from  a  great  variation  of  density  in  the 
planet  in  different  parts. 

238.  JUPITER  is  distinguished  from  all  the  other  plan- 
ets  by   his   vast   magnitude.     His   diameter  is  89,000 
miles,  and  his  volume   1280  times  that  of  the  earth. 
His  figure  is  strikingly  spheroidal,  the  equatorial  being 
larger  than  the  polar  diameter  in  the  proportion  of  107 
to  100.     Such  a  figure  might  naturally   be   expected 
from  the  rapidity  of  his  diurnal  rotation,  which  is  ac- 
complished in  about  10  hours.     A  place  on  the  equa- 
tor of  Jupiter  must  turn  27  times  as  fast  |is  on  the  ter- 
restrial equator.     The  distance  of  Jupiter  from  the  sun 
is  nearly  490,000,000  miles,  and  his  revolution  around 
the  sun  occupies  nearly  12  years. 

239.  The  view  of  Jupiter  through  a  good  telescope, 
(Fig.  43,)  is  one  of  the  most  magnificent  and  interesting 
spectacles  in  astronomy.     The  disk  expands  into  a  large 

Fig.  43. 


and  bright  orb  like  the  full  moon ;  the  spheroidal  figure 
wtych  theory  assigns  to  revolving  spheres,  is  here  pal- 


238.  Jupiter. — State  his  diameter,  volume,  figure,  revolu- 
tion on  his  axis,  velocity  of  his  equator,  distance  from  the  sun, 
periodic  time. 


JUPITER*  187 

pably  exhibited  to  the  eye ;  across  the  disk,  arranged 
in  parallel  stripes,  are  discerned  several  dusky  bands, 
called  belts ;  and  four  bright  satellites,  always  in  at- 
tendance, and  ever  varying  their  positions,  compose  a 
splendid  retinue.  Indeed,  astronomers  gaze  with  pecu- 
liar interest  on  Jupiter  and  his  moons,  as  affording  a 
miniature  representation  of  the  whole  solar  system, 
repeating  on  a  smaller  scale,  the  same  revolutions,  and 
exemplifying,  in  a  manner  more  within  the  compass 
of  our  observation,  the  same  laws  as  regulate  the 
entire  assemblage  of  sun  and  planets. 

240.  The  Belts  of  Jupiter  are  variable  in  their  num- 
ber and  dimensions.    With  the  smaller  telescopes,  only 
one  or  two  are  seen  across  the  equatorial  regions  ;  but 
with  more  powerful  instruments,  the  number  is  in- 
creased, covering  a  great  part  of  the  whole  disk.    Dif- 
ferent opinions  have  been  entertained  by  astronomers 
respecting  the  cause  of  the  belts  ;  but  they  have  gen- 
erally been  regarded  as  clouds  formed  in  the   atmo- 
sphere of  the  planet,  agitated  by  winds,  as  is  indicated 
by  their  frequent  changes,  and  made  to  assume  the 
form  of  belts  parallel  to  the  equator  by  currents  that 
circulate  around  the  planet  like  the  trade  winds  and 
other  currents  that  circulate  around  our  globe.     Sir 
John  Herschel  supposes  that  the  belts  are  not  ranges 
of  clouds,  but  portions  of  the  planet  itself  brought  into 
view  by  the  removal  of  clouds  and  mists,  that  exist  in 
the  atmosphere  of  the  planet  through  which  are  open- 
ings made  by  currents  circulating  around  Jupiter. 

241.  The  Satellites  of  Jupiter  may  be  seen  with  a 
telescope  of  very  moderate  powers.     Even  a  common 
spy  glass  will  enable  us  to  discern  them.    Indeed  one  or 
two  of  them  have  been  occasionally  seen  with  the  naked 
eye.    In  the  largest  telescopes,  they  severally  appear  as 

239.  What  does  the  telescopic  view  of  Jupiter  exhibit  ? 
Why  do  astronomers  regard  it  with  so  much  interest  ? 

240.  Describe  Jupiter's  Belts — to  what  are  thgx  ascribed  ? 

Bh 

OF  T;I-. 


UNIVERSITY   j 
•/*... P!-.       J 


168 


THE  PLANETS. 


bright  as  Sirius.  With  such  an  instrument,  the  view  of 
Jupiter  with  his  moons  and  belts  is  truly  a  magnificent 
spectacle,  a  world  within  itself.  As  the  orbits  of  the 
satellites  do  not  deviate  far  from  the  plane  of  the  eclip- 
tic, and  but  little  from  the  equator  of  the  planet,  they 
are  usually  seen  in  nearly  a  straight  line  with  each  other 
extending  across  the  central  part  of  the  disk. 

242.  Jupiter's  satellites  are  distinguished  from  one 
another  by  the  denominations  of  first,  second,  third,  and 
fourth,  according  to  their  relative  distances  from  Jupiter, 
the  first  being  that  which  is  nearest  to  him.  Their  ap- 
parent motion  is  oscillatory,  like  that  of  a  pendulum, 
going  alternately  from  their  greatest  elongation  on  one 
side  to  their  greatest  elongation  on  the  other,  sometimes 
in  a  straight  line,  and  sometimes  in  an  elliptical  curve, 
according  to  the  different  points  of  view  in  which  we 
observe  them  from  the  earth.  They  are  sometimes  sta- 
tionary ;  their  motion  is  alternately  direct  and  retro- 
grade ;  and,  in  short,  they  exhibit  in  miniature  all  the 
phenomena  of  the  planetary  system.  Various  partic- 
ulars of  the  system  are  exhibited  in  the  following  table. 
The  distances  are  given  in  radii  of  the  primary. 


Satellite. 

Diameter. 

Mean  Distance. 

Sidereal  Revolution. 

1 

2 
3 
4 

2508 
2068 
3377 

2890 

6.04853 
9.62347 
15.35024 
26.99835 

Id.     18h.  28m. 
3         13      14 
7           3      43 
16         16      32 

Hence  it  appears,  first,  that  Jupiter's  satellites  are  all 
except  the  second,  somewhat  larger  than  the  moon,  but 
that  the  second  satellite  is  the  smallest,  and  the  third 
the  largest  of  the  whole,  but  the  diameter  of  the  latter 
is  only  about  -fa  part  of  that  of  the  primary ;  secondly, 
that  the  distance  of  the  innermost  satellite  from  the  planet 


241.  How  do  the  satellites  appear  to  the  telescope  ? 

242.  Describe  the  motions  of  the  satellites — magnitudes — 
distances — periods  of  revolution. 


JUPITER.  189 

is  three  times  his  diameter,  while  that  of  the  outermost 
satellite  is  nearly  fourteen  times  his  diameter  ;  thirdly, 
that  the  first  satellite  completes  his  revolution  around  the 
primary  in  one  day  and  three  fourths,  while  the  fourth 
satellite  requires  nearly  sixteen  and  three  fourths  days. 

243.  The  orbits  of  the  satellites  are  nearly  or  quite 
circular,  and  deviate  but  little  from  the  plane  of  the 
planet's  equator,  and  of  course  are  but  slightly  inclined 
to  the  plane  of  its  orbit.     They  are,  therefore,  in  a  sim- 
ilar situation  with  respect  to  Jupiter  as  the  moon  would 
be  with  respect  to  the  earth  if  her  orbit  nearly  coincided 
with  the  ecliptic,  in  which  case  she  would  undergo  an 
eclipse  at  every  opposition. 

244.  The  eclipses  of  Jupiter's  satellites,  in  their  gen- 
eral conception,  are  perfectly  analogous  to  those  of  the 
moon,  but  in  their  detail  they  differ  in  several  particulars. 
Owing  to  the  much  greater  distance  of  Jupiter  from  the 
sun,  and  its  greater  magnitude,  the  cone  of  its  shadow  is 
much  longer  and  larger  than  that  of  the  earth.     On  this 
account,  as  well  as  on  account  of  the  little  inclination  of 
their  orbits  to  that  of  their  primary,  the  three  inner  sat- 
ellites of  Jupiter  pass  through  the  shadow,  and  are  totally 
eclipsed  at  every  revolution.     The  fourth  satellite,  ow- 
ing to  the  greater  inclination  of  its  orbit,  sometimes 
though  rarely  escapes  eclipse,  and  sometimes  merely 
grazes  the  limits  of   the  shadow  or  suffers   a  partial 
eclipse.     These  eclipses,  moreover,  are  not  seen,  as  is 
the  case  with  those  of  the  moon,  from  the  center  of 
their  motion,  but  from  a  remote  station,  and  one  whose 
situation  with  respect  to  the  line  of  the  shadow  is  vari- 
able.    This,  of  course,  makes  no  difference  in  the  times 
of  the  eclipses,  but  a  very  great  one  in  their  visibility, 


243.  What  is  the  shape  of  their  orbits  ?     How  situated  with 
regard  to  the  plane  of  the  planet's  orbit  ? 

244.  Describe  the  phenomena  of  their  eclipses.     Which  of 
them  escapes  an  eclipse  ?    Are  these  eclipses  seen  in  different 
parts  of  the  earth  at  the  same  moment  of  absolute  time  t 


190  THE  PLANETS. 

and  in  their  apparent  situations  with  respect  to  the 
planet  at  the  moment  of  their  entering  or  quitting  the 
shadow. 

245.  The  eclipses  of  Jupiter's  satellites  present  some 
curious  phenomena,  which  will  be  understood  from  th« 
following  diagrams. 

Fig.  44. 


Let  A,  B,  C,  I),  (Fig.  44,)  represent  the  earth  in  dif- 
ferent parts  of  its  orbit ;  J,  Jupiter  in  his  orbit  sur- 
rounded by  his  four  satellites  the  orbits  of  which  are 
marked  1,  2,  3,  4.  At  a  the  first  satellite  enters  the 
shadow  of  the  planet,  and  emerges  from  it  at  b,  and  ad- 
vances to  its  greatest  elongation  at  c.  The  other  satellites 
traverse  the  shadow  in  a  similar  .manner.  These  ap- 
pearances will  be  modified  by  the  place  the  earth  hap- 
pens to  occupy  in  its  orbit,  being  greatly  altered  by  per- 
spective ;  but  their  appearances  for  any  given  night  as 
exhibited  at  Greenwich,  are  calculated  and  accurately 
laid  down  in  the  Nautical  Almanac. 

When  one  of  the  satellites  is  passing  between  Jupiter 
and  the  sun  it  casts  its  shadow  on  the  primary  as  the 


245.  Describe  the  phenomena  of  the  eclipses  from  figure  44. 
Will  these  appearances  be  affected  by  the  relative  position  of 
the  earth,  with  respect  to  the  planet  ?  Does  the  shadow  of  a 
satellite  or  the  satellite  itself  ever  make  a  transit  across  the 
disk  of  the  planet  ? 


JUPITER.  191 

moon  casts  its  shadow  on  the  earth  in  a  solar  eclipse. 
We  see  with  the  telescope,  the  shadow  traversing  the 
disk.  Sometimes  the  satellite  itself  is  seen  projected  on 
the  disk  ;  but  being  illuminated  as  well  as  the  primary, 
it  is  not  so  easily  distinguished  as  Venus  or  Mercury, 
when  seen  on  the  sun's  disk,  since,  at  the  time  of  their 
transits,  their  dark  sides  are  turned  towards  us.  The 
manner  in  which  these  phenomena  take  place,  as  seen 
from  the  earth  in  the  several  positions,  A,  B,  C,  D,  may 
be  conceived  by  attentively  inspecting  the  figure.  It 
will  be  seen,  that  when  the  earth  is  at  A  or  C,  the  im- 
mersions and  emersions  must  take  place  close  to  the  disk 
of  the  planet,  but  that,  in  other  positions  of  the  earth,  as 
at  B  or  D,  the  satellite  will  be  seen  to  enter  and  leave 
the  shadow  at  some  distance  from  the  primary. 

246.  The  eclipses  of  Jupiter's  satellites  have  been 
studied  with  great  attention  by  astronomers,  on  account 
of  their  affording  one  of  the  easiest  methods  of  deter- 
mining the  longitude.  On  this  subject  Sir  J.  Herschel 
remarks :  The  discovery  of  Jupiter's  satellites  by  Gali- 
leo, which  was  one  of  the  first  fruits  of  the  invention  of 
the  telescope,  forms  one  of  the  most  memorable  epochs 
in  the  history  of  astronomy.  The  first  astronomical  so- 
lution of  the  great  problem  of  "  the  longitude," — the 
most  important  problem  for  the  interests  of  mankind 
that  has  ever  been  brought  under  the  dominion  of  strict 
scientific  principles,  dates  immediately  from  their  dis- 
covery. The  final  and  conclusive  establishment  of  the 
Copernican  system  of  astronomy,  may  also  be  considered 
as  referable  to  the  discovery  and  study  of  this  exquisite 
miniature  system,  in  which  the  laws  of  the  planetary 
motions,  as  ascertained  by  Kepler,  and  especially  that 
which  connects  their  periods  and  distances,  were  speed- 
ily traced,  and  found  to  be  satisfactorily  maintained. 


246.  Why  have  the  eclipses  of  Jupiter's  satellites  been  stud- 
ied with  so  much  attention  ?  Who  first  discovered  these  eclip- 
ses ?  What  bearing  has  the  system  of  Jupiter  and  his  satel- 
lites upon  the  Copernican  system  of  astronomy  ? 


192  THE  PLANETS. 

•a* 

247.  The  entrance  of  one  of  Jupiter's  satellites  into 
the  shadow  of  the  primary  being  seen  like  the  entrance 
of  the  moon  into  the  earth's  shadow,  at  the  same  mo- 
ment of  absolute  time,  at  all  places  where  the  planet  is 
visible,  and  being  wholly  independent  of  parallax ;  be- 
ing, moreover,  predicted  beforehand  with  great  accuracy 
for  the  instant  of  its  occurrence  at  Greenwich,  and  given 
in  the  Nautical  Almanac ;  this  would  seem  to  be  one  of 
those  events  (Art.  188,)  which  are  peculiarly  adapted  for 
finding  the  longitude.  It  must  be  remarked,  however, 
that  the  extinction  of  light  in  the  satellite  at  its  immer- 
sion, and  the  recovery  of  its  light  at  its  emersion,  are  not 
instantaneous  but  gradual;  for  the  satellite,  like  the 
moon,  occupies  some  time  in  entering  into  the  shadow 
or  in  emerging  from  it,  which  occasions  a  progressive 
dimunition  or  increase  of  light.  The  better  the  light 
afforded  by  the  telescope  with  which  the  observation  is 
made,  the  later  the  satellite  will  be  seen  at  its  immer- 
sion, and  the  sooner  at  its  emersion.*  In  noting  the 
eclipses  even  of  the  first  satellite,  the  time  must  be  con- 
sidered as  uncertain  to  the  amount  of  20  or  30  seconds  ; 
and  those  of  the  other  satellites  involve  still  greater  un- 
certainty. Two  observers,  in  the  same  room,  observing 
with  different  telescopes  the  same  eclipse,  will  frequently 
disagree  in  noting  its  time  to  the  amount  of  15  or  20 
seconds ;  and  the  difference  will  be  always  the  same 
way. 

Better  methods,  therefore,  of  finding  the  longitude  are 
now  employed,  although  the  facility  with  which  the 
necessary  observations  can  be  made,  and  the  little  calcu- 
lation required,  still  render  this  method  eligible  in  many 


247.  Explain  how  these  eclipses  are  used  in  finding  the  lon- 
gitude. What  imperfections  attend  this  method  ?  Is  this  meth- 
od much  employed  at  present  ?  Why  can  it  not  be  used  at 
sea? 


*  This  is  the  reason  why  observers  are  directed  in  the  Nautical  Al- 
manac to  use  telescopes  of  ?.  certain  power. 


SATURN.  193 

cases  where  extreme  accuracy  is  not  important.  As  a 
telescope  is  essential  for  observing  an  eclipse  of  one  of 
the  satellites,  it  is  obvious  that  this  method  cannot  be 
practiced  at  sea. 

248.  The  grand  discovery  of  the  progressive  motion 
of  light,  was  first  made  by  observations  on  the  eclipses 
of  Jupiter's  satellites.     In  the  year  1 675,  it  was  remarked 
by  Roemer,  a  Danish  astronomer,  on  comparing  together 
observations  of  these  eclipses  during  many  successive 
years,  that  they  take  place  sooner  by  about  sixteen  min- 
utes, (16m.26s.6)  when  the  earth  is  on  the  same  side  of 
the  sun  with  the  planet,  than  when  she  is  on  the  oppo- 
site side.     This  difference  he  ascribed  to  the  progressive 
motion  of  light,  which  takes  that  time  to  pass  through  the 
diameter  of  the  earth's  orbit,  making  the  velocity  of  light 
about  1 92,000  miles  per  second.    So  great  a  velocity  star- 
tled astronomers  at  first,  and  produced  some  degree  of 
distrust  of  this  explanation  of  the  phenomenon ;  but  the 
subsequent  discovery  of  what  is  called  the  aberration  of 
light,  led  to  an  independent  estimation  of  the  velocity  of 
light  with  almost  precisely  the  same  result. 

249.  SATURN  comes  next  in  the  series  as  we  recede 
from  the  sun,  and  has,  like  Jupiter,  a  system  within  it- 
self, on  a  scale  of  great  magnificence.     In  size  it  is,  next 
to  Jupiter,  the  largest  of  the  planets,  being  79,000  miles 
in  diameter,  or  about  1,000  times  as  large  as  the  earth. 
It  has  likewise  belts  on  its  surface  and  is  attended  by 
seven  satellites.     But  a  still  more  wonderfnl  appendage 
is  its  Ring,  a  broad  wheel  encompassing  the  planet  at  a 
great  distance  from  it.     We  have  already  intimated  that 
Saturn's  system  is  on  a  grand  scale.     As,  however,  Sat- 


248.  How  was  the  progressive  motion  of  light  first  discovered  ? 
Explain  the  manner  of  the  discovery.  How  long  is  light  in 
traversing  the  diameter  of  the  earth's  orbit  ?  What  is  its  ve- 
locity per  second  ?  How  does  this  agree  with  that  derived 
from  the  aberration  of  light  ? 

17 


194  THE    PLANETS. 

urn  is  distant  from  us  nearly  900,000,000  miles,  we  are 
unable  to  obtain  the  same  clear  and  striking  views  of 
his  phenomena  as  we  do  of  the  phenomena  of  Jupiter,  al- 
though they  really  present  a  more  wonderful  mechanism. 

250.  Saturn's  ring,  when  viewed  with  telescopes  of 
a  high  power,  is  found  to  consist  of  two  concentric  rings, 
separated  from  each  other  by  a  dark  space.  Although 
this  division  of  the  rings  appears  to  us,  on  account  of 
our  immense  distance,  as  only  a  fine  line,  yet  it  is  in  re- 
ality an  interval  of  not  less  than  about  1800  miles.  The 
dimensions  of  the  whole  system  are  in  round  numbers 
as  follows : 

Miles. 

Diameter  of  the  planet,  .  .  .  .  V)  79,000 
From  the  surface  of  the  planet  to  the  inner  ring,  20,000 
Breadth  of  the  inner  ring,  ....  17,000 
Interval  between  the  rings, ....  1,800 

Breadth  of  the  outer  ring,  ....  10,500 
Extreme  dimensions  from  outside  to  outside,  176,000 

Fig.  45. 


The  figure  represents  Saturn  as  it  appears  to  a  power- 
ful telescope,  surrounded  by  its  rings,  and  having  its  body 
striped  with  dark  belts,  somewhat  similar  but  broader 


249.  Saturn. — State  his  diameter  and  volume,  number  of 
•atellites,  ring,  distance  from  the  sun. 


SATURN.  195 

and  less  strongly  marked  than  those  of  Jupiter,  and 
owing  doubtless  to  a  similar  cause.  That  the  ring  is  a 
solid  opake  substance,  is  shown  by  its  throwing  its  shad- 
ow on  the  body  of  the  planet  on  the  side  nearest  the  sun 
and  on  the  other  side  receiving  that  of  the  body.  From 
the  parallelism  of  the  belts  with  the  plane  of  the  ring, 
it  may  be  conjectured  that  the  axis  of  rotation  of  the 
planet  is  perpendicular  to  that  plane ;  and  this  conjec- 
ture is  confirmed  by  the  occasional  appearance  of  exten- 
sive dusky  spots  on  its  surface,  which  when  watched 
indicate  a  rotation  parallel  to  the  ring  in  lOh.  29m.  17s. 
This  motion,  it  will  be  remarked,  is  nearly  the  same 
with  the  diurnal  motion  of  Jupiter,  subjecting  places  on 
the  equator  of  the  planet  to  a  very  swift  revolution,  and 
occasioning  a  high  degree  of  compression  at  the  poles, 
the  equatorial  being  to  the  polar  diameter  in  the  high 
ratio  of  11  to  10.  It  requires  a  telescope  of  high  mag- 
nifying powers  and  a  strong  light,  to  give  a  full  and 
striking  view  of  Saturn  with  his  rings  and  belts  and  sat- 
tellites ;  for  we  must  bear  in  mind,  that  in  the  distance 
of  Saturn  one  second  of  angular  measurement  corres- 
ponds to  4,000  miles,  a  space  equal  to  the  semi-diameter 
of  our  globe.  But  with  a  telescope  of  moderate  powers, 
the  leading  phenomena  of  the  ring  itself  may  be  ob- 
served. 

251.  Saturn1  s  ring,  in  its  revolution  awund  the  sun, 
always  remains  parallel  to  itself. 

If  we  hold  opposite  to  the  eye  a  circular  ring  or  disk 
like  a  piece  of  coin,  it  will  appear  as  a  complete  circle 
when  it  is  at  right  angles  to  the  axis  of  vision,  but  when 
oblique  to  that  axis  it  will  be  projected  into  an  ellipse 


250.  How  is  the  ring  divided  by  large  telescopes?  State  the 
several  dimensions  of  Saturn  and  his  rings.  Describe  tho 
figure.  i|pw  is  the  ring  inferred  to  be  a  solid  opake  sub- 
stance ?  In  what  time  does  Saturn  revolve  on  his  axis  ?  What 
figure  does  this  give  to  the  planet  ?  What  kind  of  telescope  is 
required  to  see  the  phenomena  of  Saturn  to  advantage  ? 


196  THfc  PLANETS. 

more  ,and  more  flattened  as  its  obliquity  is  increased, 
until,  when  its  plane  coincides  with  the  axis  of  vision, 
it  is  projected  into  a  straight  line.  Let  us  place  on  the 
table  a  lamp  to  represent  the  sun,  and  holding  the  ring 
at  a  certain  distance  inclined  a  little  towards  the  lamp, 
let  us  carry  it  round  the  lamp  always  keeping  it  parallel 
to  itself.  During  its  revolution  it  will  twice  present  its 
edge  to  the  lamp  at  opposite  points,  and  twice  at  places 
90°  distant  from  those  points,  it  will  present  its  broadest 
face  towards  the  lamp.  At  intermediate  points,  it  will 
exhibit  an  ellipse  more  or  less  open,  according  as  it  is 
nearer  one  or  the  other  of  the  preceding  positions.  It 
will  be  seen  also  that  in  one  half  of  the  revolution  the 
lamp  shines  on  one  side  of  the  ring,  and  in  the  other 
half  of  the  revolution  on  the  other  side.  Such  would 
be  the  successive  appearances  of  Saturn's  ring  to  a  spec- 
tator on  the  sun ;  and  since  the  earth  is,  in  respect  to 
so  distant  a  body  as  Saturn,  very  near  the  sun,  these 
appearances  are  presented  to  us  in  nearly  the  same  man- 
ner as  though  we  viewed  them  from  the  sun.  Accord 
dingly,  we  sometimes  see  Saturn's  ring  under  the  form 
of  a  broad  ellipse,  which  grows  continually  more  and 
more  acute  until  it  passes  into  a  line,  and  we  either  lose 
sight  of  it  altogether,  or  by  the  aid  of  the  most  power- 
ful telescopes,  we  see  it  as  a  fine  thread  of  light  drawn 
across  the  disk  and  projecting  out  from  it  on  each  side. 
As  the  whole  revolution  occupies  30  years,  and  the  edge 
is  presented  to  the  sun  twice  in  the  revolution,  this  last 
phenomenon,  namely,  the  disappearance  of  the  ring, 
takes  place  every  15  years. 

252.  The  learner  may  perhaps  gain  a  clearer  idea  of 
the  foregoing  appearances  from  the  following  diagram  : 

Let  A,  B,  C,  &c.  represent  successive  positions  of  Sat- 
urn and  his  ring  in  different  parts  of  his  orbit,  while 


251.  How  is  the  position  of  the  ring  with  respdfct  to  itself 
m  all  parts  of  its  revolution  ?  How  may  the  various  appear- 
ances of  the  ring  be  represented  ? 


SATURN. 


197 


abc  represents  the  orbit  of  the  earth.*  Were  the  ring 
when  at  C  and  G  perpendicular  to  the  CG,  it  would  be 
seen  by  a  spectator  situated  at  a  or  d  a  perfect  circle, 
but  being  inclined  to  the  line  of  vision  28°  4',  it  is  pro- 
jected into  an  ellipse.  This  ellipse  contracts  in  breadth 


46. 


as  the  ring  passes  towards  its  nodes  at  A  and  E,  where 
it  dwindles  into  a  straight  line.  From  E  to  G  the  ring 
opens  again,  becomes  broadest  at  G,  and  again  contracts 
till  it  becomes  a  straight  line  at  A,  and  from  this  point 
expands  till  it  recovers  its  original  breadth  at  C.  These 
successive  appearances  are  all  exhibited  to  a  telescope  of 
moderate  powers.  The  ring  is  extremely  thin,  since  the 
smallest  satellite,  when  projected  on  it,  more  than  covers 
it.  The  thickness  is  estimated  at  100  miles. 

253.  Saturn's  ring  shines  wholly  by  reflected  light 
derived  from  the  sun.  This  is  evident  from  the  fact, 
that  that  side  only  which  is  turned  towards  the  sun  is 
enlightened  ;  and  it  is  remarkable,  that  the  illumination 
of  the  ring  is  greater  than  that  of  the  planet  itself,  but 


252.  Explain  the  revolution  of  the  ring  by  figure  46. 

253.  Whence  does  the  ring  derive  its  light  ?     What  causes 
occasion  the  disappearance  of  the  ring  ?     At  what  intervals 
do  these  disappearances  occur  ? 


*  It  may  be  remarked  by  the  learner,  that  .these  orbits  are  made  so 
elliptical,  not  to  represent  the  eccentricity  of  either  the  earth's  or  Sat- 
urn's 01  bit,  but  merely  as  the  projection  of  circles  seen  very  obliquely, 

17* 


198  THE  PLANETS. 

the  outer  ring  is  less  bright  than  the  inner.  Although, 
as  we  have  already  remarked,  we  view  Saturn's  ring 
nearly  as  though  we  saw  it  from  the  sun,  yet  the  plane 
of  the  ring  produced  may  pass  between  the  earth  and 
the  sun,  in  which  case  also  the  ring  becomes  invisi- 
ble, the  illuminated  side  being  wholly  turned  from  us. 
Thus  when  the  ring  is  approaching  its  node  at  E,  a  spec- 
tator at  a  would  have  the  dark  side  of  the  ring  presented 
to  him.  The  ring  was  invisible  in  1833,  and  will  be 
invisible  again  in  1847.  The  northern  side  of  the  ring 
will  be  seen  until  1845,  when  the  southern  side  will 
come  into  view. 

It  appears,  therefore,  that  there  are  three  causes  for 
the  disappearance  of  Saturn's  ring ;  first,  when  the  edge 
of  the  ring  is  presented  to  the  sun  ;  secondly,  when  the 
edge  is  presented  to  the  earth  ;  and  thirdly,  when  the  un- 
illuminated  side  is  towards  the  earth. 

254.  Saturn's  ring  revolves  in  its  own  plane  in  about 
10i  hours,  (lOh.  32m.  15s.4).     La  Place  inferred  this 
from  the  doctrine  of  universal  gravitation.     He  proved 
that  such  a  rotation  was  necessary,  otherwise  the  matter 
of  which  the  ring  is  composed  would  be  precipitated 
upon  its  primary.     He  showed  that  in  order  to  sustain 
itself,  its  period  of  rotation  must  be  equal  to  the  time  of 
revolution  of  a  satellite,  circulating  around  Saturn  at  a 
distance  from  it  equal  to  that  of  the  middle  .of  the  ring, 
which  period  would  be  about  10^  hours.     By  means  of 
spots  in  the  ring,  Dr.  Herschel  followed  the  ring  in  its 
rotation,  and  actually  found  its  period  to  be  the  same  as 
assigned  by  La  Place, — a  coincidence  which  beautifully 
exemplifies  the  harmony  of  truth. 

255.  Although  the  rings  are  very  nearly  concentric  with 
the  planet,  yet  recent  measurements  of  extreme  delicacy 


254  In  what  time  does  the  ring  revolve  in  its  own  plane  ? 
How  was  this  re  volution  inferred  to  exist  before  it  was  actually 
observed  ? 


SATURN.  199 

have  demonstrated,  that  the  coincidence  is  not  mathe- 
matically exact,  but  that  the  center  of  gravity  of 'the  rings 
describes  around  that  of  the  body  a  very  minute  orbit. 
This  fact,  unimportant  as  it  may  seem,  is  of  the  utmost 
consequence  to  the  stability  of  the  system  of  rings.  *  Sup- 
posing them  mathematically  perfect  in  their  circular  form, 
and  exactly  concentric  with  the  planet,  it  is  demonstrable 
that  they  would  form  (in  spite  of  their  centrifugal  force) 
a  system  in  a  state  of  unstable  equilibrium,  which  the 
slightest  external  power  would  subvert — not  by  causing 
a  rupture  in  the  substance  of  the  rings — but  by  precip- 
itating them  unbroken  on  the  surface  of  the  planet. 
The  ring  may  be  supposed  of  an  unequal  breadth  in  its 
different  parts,  and  as  consisting  of  irregular  solids, 
whose  common  center  of  gravity  does  not  coincide  with 
the  center  of  the  figure.  Were  it  not  for  this  distribu- 
tion of  matter,  its  equilibrium  would  be  destroyed  by 
the  slightest  force,  such  as  the  attraction  of  a  satellite, 
and  the  ring  would  finally  precipitate  itself  upon  the 
planet. 

As  the  smallest  difference  of  velocity  between  the 
planet  and  its  rings  must  infallibly  precipitate  the  rings 
upon  the  planet,  never  more  to  separate,  it  follows  either 
that  their  motions  in  their  common  orbit  round  the  sun, 
must  have  been  adjusted  to  each  other  by  an  external 
power,  with  the  minutest  precision,  or  that  the  rings 
must  have  been  formed  about  the  planet  while  subject 
to  their  common  orbitual  motion,  and  under  the  full  and 
free  influence  of  all  the  acting  forces. 

The  rings  of  Saturn  must  present  a  magnificent  spec- 
tacle from  those  regions  of  the  planet  which  lie  on  their 
enlightened  sides,  appearing  as  vast  arches  spanning  the 
sky  from  horizon  to  horizon,  and  holding  an  invariable 
situation  among  the  stars.  On  the  other  hand,  in  the 
region  beneath  the  dark  side,  a  solar  eclipse  of  15  years 


255.  Are  the  rings  concentric  with  the  planet  ?  What  ad- 
vantage results  from  this  arrangement  ?  How  must  the  rings 
appear  when  seen  from  the  planets  ? 


200  THE  PLANETS. 

in  duration,  under  their  shadow,  must  afford  (to  our 
ideas)  an  inhospitable  abode  to  animated  beings,  but  ill 
compensated  by  the  full  light  of  its  satellites.  But  we 
shall  do  wrong  to  judge  of  the  fitness  or  unfitness  of 
their  condition  from  what  we  see  around  us,  when,  per- 
haps, the  very  combinations  which  convey  to  our  minds 
only  images  of  horror  may  be  in  reality  theatres  of  the 
most  striking  and  glorious  displays  of  beneficent  con- 
trivance. (Sir  J.  Herschel.) 

256.  Saturn  is  attended  by  seven  satellites.  Although 
bodies  of  considerable  size,  their  great  distance  prevents 
their  being  visible  to  any  telescopes  but  such  as  afford  a 
strong  light  and  high  magnifying  powers.  The  outer- 
most satellite  is  distant  from  the  planet  more  than  30 
times  the  planet's  diameter,  and  is  by  far  the  largest  of 
the  whole.  It  is  the  only  one  of  the  series  whose  theory 
has  been  investigated  further  than  suffices  to  verify  Kep- 
ler's law  of  the  periodic  times,  which  is  found  to  hold 
food  here  as  well  as  in  the  system  of  Jupiter.  It  ex- 
ibits,  like  the  satellites  of  Jupiter,  periodic  variations  of 
light,  which  prove  its  revolution  on  its  axis  in  the  time 
of  a  sidereal  revolution  about  Saturn.  The  next  satellite 
in  order,  proceeding  inwards,  is  tolerably  conspicuous  ; 
the  three  next  are  very  minute,  and  require  pretty  pow- 
erful telescopes  to  see  them ;  while  the  two  interior  sat- 
ellites, which  just  skirt  the  edge  of  the  ring,  and  move 
exactly  in  its  plane,  have  never  been  discovered  but  with 
the  most  powerful  telescopes  which  human  art  has  yet 
constructed,  and  then  only  under  peculiar  circumstances. 
At  the  time  of  the  disappearance  of  the  rings  (to  ordinary 
telescopes)  they  were  seen  by  Sir  William  Herschel 
with  his  great  telescope,  projected  along  the  edge  of  the  :  •  Jjj 
ring,  and  threading  like  beads  the  thin  fibre  of  light  to 


256.  What  is  the  number  of  Saturn's  satellites  ?  How  far 
distant  from  the  planet  is  the  outermost  satellite  ?  Do  the  sat- 
ellites follow  Kepler's  third  law  ?  Which  of  the  satellites  are 
easily  seen  ?  Do  they  undergo  eclipses  ? 


URANUS.  201 

which  the  ring  is  then  reduced.  Owing  to  the  obliquity 
of  the  ring,  and  of  the  orbits  of  the  satellites  to  that  of 
their  primary,  there  are  no  eclipses  of  the  satellites,  the 
two  interior  ones  excepted,  until  near  the  time  when  the 
ring  is  seen  edgewise. 

257.  URANUS  is  the  remotest  planet  belonging  to  our 
system,  and  is  rarely  visible  except  to  the  telescope.     Al- 
though his  diameter  is  more  than  four  times  that  of  the 
earth,  (35,112  miles,)  yet  his  distance   from  the  sun  is 
likewise  nineteen  times  as  great  as  the  earth's  distance, 
or  about   1,800,000,000  miles.     His  revolution  around 
the  sun  occupies  nearly  84  years,  so  that  his  position  in 
the  heavens  for  several  years  in  succession  is  nearly  sta- 
tionary.    His  path  lies  very  nearly  in  the  ecliptic,  being 
inclined  to  it  less  than  one  degree,  (46X  28".44.) 

The  sun  himself  when  seen  from  Uranus  dwinflles  al- 
most to  a  star,  subtending  as  it  does  an  angle  of  only 
1/  40"  ;  so  that  the  surface  of  the  sun  would  appear 
there  400  times  less  than  it  does  to  us. 

This  planet  was  discovered  by  Sir  William  Herschel 
on  the  1 3th  of  March  1781.  His  attention  was  attracted 
to  it  by  the  largeness  of  its  disk  in  the  telescope  ;  and 
finding  that  it  shifted  its  place  among  the  stars,  he  at 
first  took  it  for  a  comet,  but  soon  perceived  that  its  orbit 
was  not  eccentric  like  the  orbits  of  comets,  but  nearly 
circular  like  those  of  the  planets.  It  was  then  recog- 
nized as  a  new  member  of  the  planetary  system,  a  con- 
clusion which  has  been  justified  by  all  succeeding  ob- 
servations. 

258.  Uranus  is  attended  by  six  satellites.     So  minute 
objects  are  they,  that  they  can  be  seen  only  by  powerful 
telescopes.     Indeed,  the  existence  of  more  than  two  is 
still   considered   as   somewhat   doubtful.     These   two, 


257.  Uranus. — State  his  diameter — distance  from  the  sun— ^ 
periodic  time — inclination  of  his  orbit.  How  would  the  sun 
appear  from  Uranus  ?  State  the  history  of  his  discovery 


602  THE  PLANETS. 

however,  offer  remarkable,  and  indeed  qui'e  unexpected 
and  unexampled  peculiarities.  Contrary  to  the  unbro- 
ken analogy  of  the  whole  planetary  system,  the  planes 
of  their  orbits  are  nearly  perpendicular  to  the  ecliptic, 
being  inclined  no  less  than  78°  58'  to  that  plane,  and  in 
these  orbits  their  motions  are  retrograde  ;  that  is,  instead 
of  advancing  from  west  to  east  around  their  primary,  as 
is  the  case  with  all  the  other  planets  and  satellites,  they 
move  in  the  opposite  direction.  With  this  exception,  all 
the  motions  of  the  planets,  whether  around  their  own 
axes,  or  around  the  sun,  are  from  west  to  east.  The  sun, 
himself,  turns  on  his  axis  from  west  to  east ;  all  the  pri- 
mary planets  revolve  around  the  sun  from  west  to  east ; 
their  revolutions  on  their  own  axes  are, also  in  the  same 
direction  ;  all  the  secondaries,  with  the  single  exception 
above-mentioned,  move  about  their  primaries  from  west 
to  east ;  and,  finally,  such  of  the  secondaries  as  have 
been  discovered  to  have  a  diurnal  revolution,  follow  the 
same  course.  Such  uniformity  among  so  many  motions, 
could  have  resulted  only  from  forces  impressed  upon 
them  by  the  same  omnipotent  hand ;  and  few  things  in 
the  creation  more  distinctly  proclaim  that  God  made  the 
world. 


THE  NEW  PLANETS,  CERES,  PALLAS,  JUNO,  AND  VESTA. 

259.  THE  commencement  of  the  present  century  was 
rendered  memorable  in  the  annals  of  astronomy,  by  the 
discovery  of  four  new  planets  between  Mars  and  Jupiter. 
Kepler,  from  some  analogy  which  he  found  to  subsist 
among  the  distances  of  the  planets  from  the  sun,  had 
long  before  suspected  the  existence  of  one  at  this  dis- 
tance ;  and  his  conjecture  was  rendered  more  probable 
by  the  discovery  of  Uranus,  which  follows  the  analogy 


258.  By  how  many  satellites  is  Uranus  attended  ?  What  is 
said  of  their  minuteness  ?  What  remarkable  peculiarities  have 
they  ?  In  what  direction  are  the  motions  of  all  the  bodies  in 
the  solar  system  ?  What  does  this  fact  indicate  with  respect  to 
their  origin  ? 


NEW  PLANETS.  203 

«>f  the  other  planets.  So  strongly,  indeed,  were  astrono- 
mers impressed  with  the  idea  that  a  planet  would  be 
found  between  Mars  and  Jupiter,  that,  in  the  hope  of 
discovering  it,  an  association  was  formed  on  the  conti 
nent  of  Europe  of-  twenty-four  observers,  who  divided 
the  sky  into  as  many  zones,  one  of  which  was  allotted 
to  each  member  of  the  association.  The  discovery  of 
the  first  of  these  bodies  was  however  made  accidentally 
by  Piazzi,  an  astronomer  of  Palermo,  on  the  first  of  Jan- 
uary, 1801.  It  was  shortly  afterwards  lost  sight  of  on 
account  of  its  proximity  to  the  sun,  and  was  not  seen 
again  until  the  close  of  the  year,  when  it  was  re-discov- 
ered in  Germany.  Piazzi  called  it  Ceres,  in  honor  of 
the  tutelary  goddess  of  Sicily  ;  and  her  emblem,  the 
sickle?,  has  been  adopted  as  its  appropriate  symbol. 

The  difficulty  of  finding  Ceres  induced  Dr.  Olbers,  of 
Bremen,  to  examine  with  particular  care  all  the  small 
stars  that  lie  near  her  path,  as  seen  from  the  earth  ;  and 
while  prosecuting  these  observations,  in  March,  1802,  he 
discovered  another  similar  body,  very  nearly  at  the  same 
distance  from  the  sun,  and  resembling  the  former  in 
many  other  particulars.  The  discoverer  gave  to  this  se- 
cond planet  the  name  of  Pallas,  choosing  for  its  symbol 
the  lance  $ ,  the  characteristic  of  Minerva. 

260.  The  most  surprising  circumstance  connected 
with  the  discovery  of  Pallas,  was  the  existence  of  two 
planets  at  nearly  the  same  distance  from  the  sun,  and 
apparently  having  a  common  node.  On  account  of  this 
singularity,  Dr.  Olbers  was  led  to  conjecture  that  Ceres 
and  Pallas  are  only  fragments  of  a  larger  planet,  which 
had  formerly  circulated  at  the  same  distance,  and  been 
shattered  by  some  internal  convulsion.  The  hypothesis 
suggested  the  probability  that  there  might  be  other  frag 


259.  Name  the  New  Planets.  When  were  they  discovered  ? 
What  had  been  conjectured  previous  to  their  discovery  ?  Who 
discovered  the  first  ?  What  is  its  name  ?  How  was  Pallas  dis  • 
covered  ? 


204  THE    PLANETS. 

ments,  whose  orbits,  however  they  might  differ  in  ec 
centricity  and  inclination,  might  be  expected  to  cross  the 
ecliptic  at  a  common  point,  or  to  have  the  same  node. 
Dr.  Olbers,  therefore,  proposed  to  examine  carefully  every 
month,  the  two  opposite  parts  of  the  heavens  in  which 
the  orbits  of  Ceres  and  Pallas  intersect  one  another,  with 
a  view  to  the  discovery  of  other  planets,  which  might 
be  sought  for  in  those  parts  with  greater  chance  of  suc- 
cess than  in  a  wider  zone,  embracing  the  entire  limits 
of  these  orbits.  Accordingly,  in  1804,  near  one  of  the 
nodes  of  Ceres  and  Pallas,  a  third  planet  was  discovered. 
This  was  called  Juno,  and  the  character  $  was  adopted 
for  its  symbol,  representing  the  starry  sceptre  of  the 
queen  of  Olympus.  Pursuing  the  same  researches,  in 
1807,  a  fourth  planet  was  discovered,  to  which  was 
given  the  name  of  Vesta,  and  for  its  symbol  the  char- 
acter ft  was  chosen — an  altar  surmounted  with  a  censer 
holding  the  sacred  fire. 

After  this  historical  sketch,  it  will  be  sufficient  to  clas- 
sify under  a  few  heads  the  most  interesting  particulars 
relating  to  the  New  Planets. 

261.  The  average  distance  of  these  bodies  from  the 
sun  is  261,000,000  miles;  and  it  is  remarkable  that 
their  orbits  are  very  near  together.  Taking  the  distance 
of  the  earth  from  the  sun  for  unity,  their  respective  dis- 
tances are  2.77,  2.77,  2.67,  2.37. 

As  they  are  found  to  be  governed,  like  the  other  mem- 
bers of  the  solar  system,  by  Kepler's  law,  that  regulates 
the  distances  and  times. of  revolution,  their  periodical 
times  are  of  course  pretty  nearly  equal,  averaging  about 
4^  years. 

In  respect  to  the  inclination  of  their  orbits,  there  is 
considerable  diversity.  The  orbit  of  Vesta  is  inclined 


260.  How  do  Ceres  and  Pallas  compare  in  distance  from  the 
sun  and  the  place  of  their  nodes  ?  What  hypothesis  did  Olbers 
adopt  ?  State  the  circumstances  connected  with  the  discovery 
of  Juno  and  Vesta. 


MOTIONS  OF  THE  PLANETARY  SYSTEM.  205 

to  the  ecliptic  only  about  7°,  while  that  of  Pallas  is  more 
than  34°.  They  all  therefore  have  a  higher  inclination 
than  the  orbits  of  the  old  planets,  and  of  course  make 
excursions  from  the  ecliptic  beyond  the  limits  of  the 
Zodiac. 

The  eccentricity  of  their  orbits  is  also,  in  general, 
greater  than  that  of  the  old  planets ;  and  the  eccentrici- 
ties of  the  orbits  of  Pallas  and  Juno  exceed  that  of  the 
orbit  of  Mercury. 

Their  small  size  constitutes  one  of  their  most  remark- 
able peculiarities.  The  difficulty  of  estimating  the  ap- 
parent diameters  of  bodies  at  once  so  very  small  and  so 
far  off,  would  lead  us  to  expect  different  results  in  the 
actual  estimates.  Accordingly,  while  Dr.  Herschel  es- 
timates the  diameter  of  Pallas  at  only  80  miles,  Schroe- 
ter  places  it  as  high  as  2,000  miles,  or  about  the  size  of 
the  moon.  The  volume  of  Vesta  is  estimated  at  only 
one  fifteen  thousandth  part  of  the  earth's,  and  her  surface 
is  only  about  equal  to  that  of  the  kingdom  of  Spain. 
These  little  bodies  are  surrounded  by  atmospheres  of 
great  extent,  some  of  which  are  uncommonly  luminous, 
and  others  appear  to  consist  of  nebulous  or  vapory  mat- 
ter. These  planets  in  general  shine  with  a  more  vivid 
light  than  might  be  expected  from  their  great  distance 
and  diminutive  size. 


CHAPTER    IX. 

MOTIONS  OF  THE  PLANETARY  SYSTEM QUANTITY  OP  MAT- 
TER IN  THE  SUN  AND  PLANETS STABILITY  OF  THE  SO- 
LAR SYSTEM. 

262.  WE  have  waited  until  the  learner  may  be  sup- 
posed to  be  familiar  with  the  contemplation  of  the  heav- 


261.  What  is  the  average  distance  of  the  New  Planets  from 
the  sun  ?  How  do  these  orbits  lie  with  respect  to  each  other? 
Are  they  subject  to  Kepler's  third  law  ?  What  is  their  average 
periodical  time  ?  What  is  said  of  the  inclination  of  their  or- 
bits ?  Also,  of  the  eccentricity  ?  What  "is  their  size  ? 

18 


206  THE  PLANETS. 

enly  bodies,  individually,  before  inviting  his  attention  to 
a  systematic  view  of  the  planets,  and  of  their  motions 
around  the  sun.  The  time  has  now  arrived  for  entering 
more  advantageously  upon  this  subject,  than  could  have 
been  done  at  an  earlier  period. 

There  are  two  methods  of  arriving  at  a  knowledge  of 
the  motions  of  the  heavenly  bodies.  One  is  to  begin 
with  the  apparent,  and  from  these  to  deduce  the  real 
motions  ;  the  other  is,  to  begin  with  considering  things 
as  they  really  are  in  nature,  and  then  to  inquire  why 
they  appear  as  they  do.  The  latter  of  these  methods  is 
by  far  the  more  eligible ;  it  is  much  easier  than  the 
other,  and  proceeding  from  the  less  difficult  to  that  which 
is  more  difficult,  from  motions  that  are  very  simple  to 
such  as  are  complicated,  it  finally  puts  the  learner  in  pos- 
session of  the  whole  machinery  of  the  heavens.  We 
shall,  in  the  first  place,  therefore,  endeavor  to  introduce 
the  learner  to  an  acquaintance  with  the  simplest  motions 
of  the  planetary  system,  and  afterwards  to  conduct  him 
gradually  through  such  as  are  more  complicated  and  dif- 
ficult. 

263.  Let  us  first  of  all  endeavor  to  acquire  an  adequate 
idea  of  absolute  space,  such  as  existed  before  the  crea- 
tion of  the"  world.  We  shall  find  it  no  easy  matter  to 
form  a  correct  notion  of  infinite  space  ;  but  let  us  fix  our 
attention,  for  some  time,  upon  extension  alone,  devoid  of 
every  thing  material,  without  light  or  life,  and  without 
bounds.  Of  such  a  space  we  could  not  predicate  the 
ideas  of  up  or  down,  east,  west,  north,  or  south,  but  all 
reference  to  our  own  horizon  (which  habit  is  the  most 
difficult  of  all  to  eradicate  from  the  mind)  must  be  com- 
pletely set  aside.  Into  such  a  void  we  would  introduce 
the  SUN.  We  would  contemplate  this  body  alone,  in 
the  midst  of  boundless  space,  and  continue  to  fix  the  at- 


262.  What  are  the  two  methods  of  studying  the  motions  of 
the  heavenly  bodies  ?  Which  method  is  bust  ?  What  motions 
will  be  first  considered  ? 


MOTIONS  OF  THE  PLANETARY  SYSTEM.         207 

tention  upon  this  object,  until  we  had  fully  settled  its 
relations  to  the  surrounding  void.  The  ideas  of  up  and 
down  would  now  present  themselves,  but  as  yet  there 
would  be  nothing  to  suggest  any  notion  of  the  cardinal 
points.  We  suppose  ourselves  next  to  be  placed  on  the 
surface  of  the  sun,  and  the  firmament  of  stars  to  be 
lighted  up.  The  slow  revolution  of  the  sun  on  his  axis, 
would  be  indicated  by  a  corresponding  movement  of  the 
stars  in  the  opposite  direction  ;  and  in  a  period  equal  to 
more  than  25  of  our  days,  the  spectator  would  see  the 
heavens  perform  a  complete  revolution  around  the  sun, 
as  he  now  sees  them  revolve  around  the  earth  once  in 
24  hours.  The  point  of  the  firmament  where  no  mo- 
tion appeared,  would  indicate  the  position  of  one  of  the 
poles,  which  being  called  North,  the  other  cardinal  points 
would  be  immediately  suggested. 

Thus  prepared,  we  may  now  enter  upon  the  conside- 
ration of  the  planetary  motions. 

264.  Standing  on  the  sun,  we  see  all  the  planets  mo 
ving  slowly  around  the  celestial  sphere,  nearly  in  the 
same  great  highway,  and  in  the  same  direction  from 
west  to  east.  They  move,  however,  with  very  unequal 
velocities.  Mercury  makes  very  perceptible  progress 
from  night  to  night,  like  the  moon  revolving  about  the 
earth,  his  daily  progress  eastward  being  one  third  as 
great  as  that  of  the  moon,  since  he  completes  his  entire 
revolution  in  about  three  months.  If  we  watch  the 
course  of  this  planet  from  night  to  night,  we  observe  it 
in  its  revolution,  to  cross  the  ecliptic  in  two  opposite 
points  of  the  heavens,  and  wander  about  7°  from  that 
plane  at  its  greatest  distance  from  it.  Knowing  the  po- 
sition of  the  orbit  of  Mercury  with  respect  to  the  ecliptic, 
we  may  now,  in  imagination,  represent  that  orbit  by  a 


263.  How  can  we  form  a  correct  idea  of  absolute  space  ? 
What  can  we  predicate  of  such  a  space  ?  If  the  sun  were  pla- 
ced in  such  a  void,  what  new  ideas  would  present  themselves  ? 
should  we  get  a  knowledge  of  the  cardinal  points  ? 


208  THE  PLANETS. 

great  circle  passing  through  the  center  of  the  planet  and 
the  center  of  the  sun,  and  cutting  the  plane  of  the  eclip- 
tic in  two  opposite  points  at  an  angle  of  7°,  We  may 
imagine  the*  intersection  of  these  two  great  circles- with 
the  celestial  vault  to  be  marked  out  in  plain  and  palpa- 
ble lines  on  the  face  of  the  sky  ;  but  we  must  bear  in 
mind  that  these  orbits  are  mere  mathematical  planes, 
having  no  permanent  existence  in  nature,  any  more  than 
the  path  of  an  eagle  flying  through  the  sky ;  and  if  we 
conceive  of  their  orbits  marked  on  the  celestial  vault, 
we  must  be  careful  to  attach  to  the  representation  the 
same  notion  as  to  a  thread  or  wire,  carried  round  to  trace 
out  the  course  pursued  by  a  horsfi.  in  a  race-ground.* 

The  planes  of  both  the  ecliptic  and  the  orbit  of  Mer- 
cury, may  be  conceived  of  as  indefinitely  extended  to  a 
great  distance  until  they  meet  the  sphere  of  the  stars ; 
but  the  lines  which  the  earth  and  Mercury  describe  in 
those  planes,  that  is,  their  orbits  may  be  conceived  of  as 
comparatively  near  to  the  sun.  Could  we  now  for  a 
moment  be  permitted  to  imagine  that  the  planes  of  the 
ecliptic,  and  of  the  orbit  of  Mercury,  were  made  of  thin 
plates  of  glass,  and  that  the  paths,of  the  respective  plan- 
ets were  marked  out  on  their  planes  in  distinct  lines,  we 
should  perceive  the  orbit  of  the  earth  to  be  alnrrtost  a  per- 
fect circle,  while  that  of  Mercury  would  appear  distinctly 
elliptical.  But  having  once  made  use  of  a  palpable  sur- 


264.  Where  must  the  spectator  be  placed  in  order  to  see  the 
real  motions  of  the  planets  ?  How  would  the  motions  of  the 
several  planets  appear  from  this  station  ?  State  the  particular 
movements  of  Mercury.  How  may  we  imagine  the  ecliptic 
and  the  orbit  of  Mercury  to  be  represented  on  the  sky  ?  How 
shall  we  conceive  of  the  planes  of  these  orbits  as  distinguished 
from  the  orbit  itself  ? 


*  It  would  seem  superfluous  to  caution  the  reader  on  so  plain  a  point, 
did  not  the  experience  of  the  instructor  constantly  show  that  young 
learners,  from  the  habit  of  seeing  the  celestial  motions  represented  in 
orreries  and  diagrams,  almost  always  fall  into  the  absurd  notion  of  con- 
sidering the  orbits  of  the  planets  as  having  a  distinct  and  independent 
existence. 


MOTIONS  OF  THE  PLANETARY  SYSTEM.  209 

face  and  visible  lines  to  aid  us  in  giving  position  and  fig- 
ure to  the  planetary  orbits,  let  us  now  throw  aside  these 
devices,  and  hereafter  conceive  of  these  planes  and  or- 
bits as  they  are  in  nature,  and  learn  to  refer  a  body  to  a 
mere  mathematical  plane,  and  to  trace  its  path  in  that 
plane  through  absolute  space. 

265.  A  clear  understanding  of  the  motions  of  Mercury 
and  of  the  relation  of  its  orbit  to  the  plane  of  the  eclip- 
tic, will  render  it  easy  to  understand  the  same  particulars 
in  regard  to  each  of  the  other  planets.  Standing  on  the 
sun  we  should  see  each  of  the  planets  pursuing  a  similar 
course  to  that  of  Mercury,  all  moving  from  west  to  east, 
with  motions  differing  from  each  other  chiefly  in  two  re- 
spects, namely,  in  their  velocities,  and  in  the  distances 
to  which  they  ever  recede  from  the  ecliptic. 

The  earth  revolves  about  the  sun  very  much  like  Ve- 
nus, and  to  a  spectator  on  the  sun,  the  motions  of  these 
two  planets  would  exhibit  much  the  same  appearances. 
We  have  supposed  the  observer  to  select  the  plane  of 
the  earth's  orbit  as  his  standard  of  reference,  and  to  see 
how  each  of  the  other  orbits  is  related  to  it ;  but  such  a 
selection  of  the  ecliptic  is  entirely  arbitrary ;  the  specta- 
tor on  the  sun,  who  views  the  motions  of  the  planets  as 
they  actually  exist  in  nature,  would  make  no  such  dis- 
tinction between  the  different  orbits,  but  merely  inquire 
how  they  were  mutually  related  to  each  other.  Taking, 
however,  the  ecliptic  as  the  plane  to  which  all  the  others 
are  referred,  we  do  not,  as  in  the  case  of  the  other  plan- 
ets, inquire  how  its  plane  is  inclined,  nor  what  are  its 
nodes,  since  it  has  neither  inclination  nor  node. 

26(K  The  attempt  to  exhibit  the  motions  of  the  solar 
system,  and  the  positions  of  the  planetary  orbits  by 


265.  If  we  stood  on  the  sun,  how  should  we  see  each  of  the 
planets  revolve  ?  Why  is  the  earth's  orbit  selected  as  the  stan- 
dard of  reference  ?  Would  the  spectator  on  the  sun  make  any 
such  distinction  ? 


210  THE  PLANETS. 

means  of  diagrams,  or  even  orreries,  is  usually  a  failure 
The  student  who  relies  exclusively  on  such  aids  as 
these,  will  acquire  ideas  on  this  subject  that  are  both  in- 
adequate and  erroneous.  They  may  aid  reflection,  but 
can  never  supply  its  place.  The  impossibility  of  rep- 
resenting things  in  their  just  proportions  will  be  evident 
when  we  reflect,  that  to  do  this,  if,  in  an  orrery,  we 
make  Mercury  as  large  as  a  cherry,  we  should  require  to 
represent  the  sun  by  a  globe  six  feet  in  diameter.  If  we 
preserve  the  same  proportions  in  regard  to  distance,  we 
must  place  Mercury  250  feet,  and  Uranus  12,500  feet, 
or  more  than  two  miles  from  the  sun.  The  mind  of  the 
student  of  astronomy  must,  therefore,  raise  itself  from 
such  imperfect  representations  of  celestial  phenomena  as 
are  afforded  by  artificial  mechanism,  and,  transferring  his 
contemplations  to  the  celestial  regions  themselves,  he 
must  conceive  of  the  sun  and  planets  as  bodies  that  bear 
an  insignificant  ratio  to  the  immense  spaces  in  which 
they  circulate,  resembling  more  a  few  little  birds  flying 
in  the  open  sky,  than  they  do  the  crowded  machinery  of 
an  orrery. 

267.  Having  acquired  as  correct  an  idea  as  we  are 
able  of  the  planetary  system,  and  of  the  positions  of  the 
orbits  with  respect  to  the  ecliptic,  let  us  next  inquire 
into  the  nature  and  causes  of  the  apparent  motions. 

The  apparent  motions  of  the  planets  are  exceedingly 
unlike  the  real  motions,  a  fact  which  is  owing  to  two 
causes  ;  first,  we  mew  them  out  of  the  center  of  their  or- 
bits ;  secondly,  we  are  ourselves  in  motion.  From  the 
first  cause,  the  apparent  places  of  the  planets  are  greatly 
changed  by  perspective ;  and  from  the  second  cause, 


266.  What  is  said  of  the  attempt  to  represent  the  positions 
and  motions  of  the  solar  system  by  diagrams  and   orreries  ? 
Give  examples. 

267.  Are  the  apparent  motions  of  the  planets  like  the  real 
motions  ?  What  makes,  them  different  ?  How  does  each  cause 
operate  1     What  is  the  heliocentric  place,  and  what  the  geo- 
centric place  of  a  planet  ? 


MOTIONS  OF  THE  PLANETARY  SYSTEM.  211 

we  attribute  to  the  planets  changes  of  place  which  arise 
from  our  own  motions  of  which  we  are  unconscious. 

The  situation  of  a  heavenly  body  as  seen  from  the 
center  of  the  sun  is  called  its  heliocentric  place  ;  as  seen 
from  the  center  of  the  earth,  its  geocentric  place.  The 
geocentric  motions  of  the  planets  must,  according  to 
what  has  just  been  said,  be  far  more  irregular  and  com- 
plicated than  the  heliocentric. 

268.  The  apparent  motions  of  the  Inferior  Planets  as 
seen  from  the  earth,  have  been  already  explained  in  ar- 
ticles 216  and  217  ;  from  which  it  appeared,  that  Mer- 
cury and  Venus  move  backwards  and  forwards  across 
the  sun,  the  former  never  being  seen  farther  than  29° 
and  the  latter  never  more  than  47°  from  that  luminary. 
It  was  also  shown  that  while  passing  from  the  greatest 
elongation  on  one  side  to  the  greatest  elongation  on  the 
other  side,  through  the  superior  conjunction,  the  apparent 
motions  of  these  planets  are  accelerated  by  the  motion 
of  the  earth  ;  but  that  while  moving  through  the  infe- 
rior conjunction,  at  which  time  their  motions  are  retro- 
grade, they  are  apparently  retarded  by  the  earth's  mo- 
tion.    Let  us  now  see  what  are  the  geocentric  motions 
of  the  Superior  Planets. 

269.  Let  A,  B,  C,  (Fig.  47,)  represent  the  earth  in 
different  positions  in  its  orbit,  and  M  a  superior  planet  as 
Mars,  and  NR  an  arc  of  the  concave  sphere  of  the 
heavens.     First,  suppose  the  planet  to  remain  at  rest  in 
M,  and  let  us  see  what  apparent  motions  it  will  receive 
from  the  real  motions  of  the  earth.     When  the  earth  is 
at  B,  it  will  see  the  planet  in  the  heavens  at  N ;  and  as 
the  earth  moves  successively  through,  C,  D,  E,  F,  the 
planet  will  appear  to  move  through  O,  P,  Q,,  R.     B  and 
F  are  the  two  points  of  greatest  elongation  of  the  earth 
from  the  sun  as  seen  from  the  planet ;  hence  between 


268.  Describe  the  apparent  motions  of  Mercury  and  Venus 
from  figure  40. 


212 


THE  PLANETS. 


these  two  points,  while  passing  through  the  part  of  her 
orbit  most  remote  from  the  planet,  (when  the  planet  is 
seen  in  superior  conjunction,)  the  earth  by  her  own  mo- 
Fig.  47. 


tion  gives  an  apparent  motion  to  the  planet  in  the  order 
of  the  signs — that  is,  the  apparent  motion  given  by  the 
earth  is  direct.  But  in  passing  from  F  to  B  through  A, 
when  the  planet  is  seen  in  opposition,  the  apparent  mo- 
tion given  to  the  planet  by  the  earth's  motion  is  from  R 
to  N,  and  is  therefore  retrograde.  As  the  arc  described 
by  the  earth,  when  the  motion  is  direct,  is  much  greater 
than  when  the  motion  is  retrograde,  while  the  apparent 
arc  of  the  heavens  described  by  the  planet  from  N  to  R 
in  the  one  case,  and  from  R  to  N  in  the  other,  is  the 


269.  Describe  the  motions  of  the  Superior  Planets  from  fig- 
ure 47.  The  planet  remaining  at  rest,  what  apparent  motions 
will  the  motion  of  the  earth  impart  to  it,  when  in  opposition  ? 
What  when  in  superior  conjunction  ? 


MOTIONS    OF    THE    PLANETARY    SYSTEM.  213 

same  in  both  cases,  the  retrograde  motion  is  much  swifter 
than  the  direct,  being  performed  in  much  less  time. 

270.  But  the  superior  planet  is  not  in  fact  at  rest,  as 
we  have  supposed,  but  is  all  the  while  moving  east- 
ward, though  with  a  slower  motion  than  the  earth.  In- 
deed, with  respect  to  the  remotest  planets  as  Saturn  and 
Uranus,  the  forward  motion  is  so  exceedingly  slow  that 
the  above  representation  is  nearly  true  for  a  single  year. 
Still,  the  effect  of  the  real  motions  of  all  the  superior 
planets  eastward,  is  to  increase  the  direct  apparent  mo- 
tion communicated  by  the  earth  and  to  diminish  the  ret- 
rograde motion. 

If  Mars  stood  still  while  the  earth  went  round  the 
sun,  then  a  second  opposition  as  at  A,  would  occur  at 
the  end  of  one  year  from  the  first ;  but  while  the  earth 
is  performing  this  circuit,  Mars  is  also  moving  the  same 
way,  more  than  half  as  fast,  so  that  when  the  earth  re- 
turns to  A,  the  planet  has  already  performed  more  than 
half  the  same  circuit,  and  will  have  completed  its  whole, 
revolution  before  the  earth  comes  up  with  it.  Indeed, 
Mars,  -after  having  been  once  seen  in  opposition,  does  not 
come  into  opposition  again  until  after  two  years  and 
fifty  days.  And  since  the  planet  is  then  comparatively 
very  near  to  us,  and  appears  very  large  and  bright,  rising 
unexpectedly  about  the  time  the  sun  sets,  he  surprises 
the  world  as  though  it  were  some  new  celestial  body. 
But  on  account  of  the  slow  progress  of  Saturn  and  Ura- 
nus, we  find  after  having  performed  one  circuit  around 
the  sun,  that  they  are  but  little  advanced  beyond  where 
we  left  them  at  the  last  opposition.  The  time  between 
one  opposition  of  Saturn  and  another  is  only  a  year  and 
thirteen  days. 

It  appears,  therefore  that  the  superior  planets  steadily 
pursue  their  course  around  the  sun,  but  that  their  appar- 


270.  How  does  the  real  motion  of  the  planet  modify  the  fore 
going  results  ?  How  in  respect  to  the  remotest  planets,  as  Ura 
nus,  and  how  in  respect  to  a  nearer  planet  as  Mars  ?  How 
often  is  Mars  in  opposition  ?  What  is  his  appearance  then  7 


214  THE    PLANETS, 

ent  retrograde  motion  when  in  opposition,  is  occasioned 
by  our  passing  by  them  with  a  swifter  motion,  like  the 
apparent  backward  motion  of  a  vessel  when  we  over- 
take it  and  pass  rapidly  by  it  in  a  steamboat. 

QUANTITY    OP   MATTER   IN    THE    SUN    AND   PLANETS. 

271.  It  would  seem  at  first  view  very  improbable  that 
an  inhabitant  of  this  earth  should  be  able  to  weigh  the 
sun  and  planets,  and  estimate  the  exact  quantity  of  mat- 
ter which  they  severally  contain.     But  the  principles  of 
Universal  Gravitation  conduct  us  to  this  result,  by  a 
process  remarkable  for  its  simplicity.    By  comparing  the 
relations  of  a  few  elements  that  are  known  to  us,  we 
ascend  to  the  knowledge  of  such  as  appeared  to  be  be- 
yond the  pale  of  human  investigation.     We  learn  the 
quantity  of  matter  in  a  body  from  the  force  of  gravity 
it  exerts,  and   this  force   is   estimated   by  its   effects. 
Hence  worlds  are  weighed  with  as  much  ease  as  a  peb- 
ble or  an  article  of  merchandise. 

272.  The  sun  contains  about  355,000  times  as  much 
matter  as  the  earth,  and  800  times  as  much  matter  as  all 
the  planets.     This  however,  is  owing  rather  to  its  great 
size  than  to  the  specific  gravity  of  its  materials,  for  the 
density  of  the  sun  is  only  one  fourth  as  great  as  that  of 
the  earth.     The  earth  is  nearly  5£  times  as  heavy  as 
water,  but  the  sun  is  only  a  little  heavier  than  that  fluid. 
The  planets  near  the  sun  are  in  general  more  dense  than 


271.  What  is  said  of  the  apparent  difficulty  of  weighing  the 
sun  and  planets  ?     What  great  principles  lead  us  to  this  re- 
sult ?     How  do  we  learn  the  quantity  of  matter  in  the  bodies 
of  the  solar  system  ? 

272.  How  much  more  matter  does  the  sun  contain  than  the 
earth  ?     How  much  more  than  all  the  planets  ?     What  is  the 
density  of  the  sun  compared  with  that  of  the  earth  ?     How 
much  heavier  is  the  earth  than  water  ?     How  much  heavier  is 
the  sun  than  water  ?     Which  of  the  planets  have  the  greatest 
density  \     How  heavy  is  Mercury  ?     How  heavy  is  Saturn  ? 


STABILITY    OP   THE    SOLAR   SYSTEM.  215 

those  more  remote ;  Mercury  being  heavier  than  lead, 
while  Saturn  is  as  light  as  a  cork.  The  decrease  in 
density  however,  is  not  entirely  regular,  since  Venus  is 
a  little  lighter  than  the  earth,  while  Jupiter  is  heavier 
than  Mars,  and  Uranus  than  Saturn. 

STABILITY    OF    THE    SOLAR    SYSTEM. 

273.  The  perturbations  occasioned  by  the  motions  of 
the  planets  by  their  action  on  each  other  are  very  nu- 
merous, since  every  body  in  the  system  exerts  an  attrac- 
tion on  every  other,  in  conformity  with  the  law  of  Uni- 
versal Gravitation.     Venus  and  Mars,  approaching  as 
they  do  at  times  comparatively  near  to  the  earth,  sen- 
sibly disturb  its  motions,  and  the  satellites  of  the  re- 
moter planets  greatly  disturb  each  other's  movements. 

274.  The  derangement  which  the  planets  produce  in 
the  motion  of  one  of  their  number  will  be  very  small  in 
the  course  of  one  revolution ;  but  this  gives  us  no  secu- 
rity that  the  derangement  may  not  become  very  large 
in  the  course  of  many  revolutions.     The  cause  acts  per- 
petually, and  it  has  the  whole  extent  of  time  to  work  in. 
Is  it  not  easily  conceivable  then,  that  in  the  lapse  of  ages, 
the  derangements  of  the  motions  of  the  planets  may 
accumulate,  the  orbits  may  change  their  form,  and  their 
mutual  distances  may  be  much  increased  or  diminished  ? 
Is  it  not  possible  that  these  changes  may  go  on  without 


273.  What  is  said  of  the  perturbations  occasioned  by  the  ac- 
tion of  the  planets  on  each  other  ?     Which  planets  in  particu- 
lar, disturb  the  motions  of  the  earth  ? 

274.  How  is  the  derangement  produced  by  the  planets  upon 
any  one  of  them,  in  a  single  revolution  ?     What  may  be  the 
ultimate  effect  of  these  disturbing  forces  ?     What  would  be 
tiie  consequence  of  increasing  the  eccentricity  of  the  earth's 
orbit — or  of  bringing  the  moon  nearer  the  earth — or  of  alter- 
ing the  positions  of  the  planets  with  respect  to  that  of  the 
earth  ?     What  changes  are  actually  going  on  in  the  motions 
of  the  heavenly  bodies  ? 


216  THE    PLANETS. 

limit,  and  end  in  the  complete  subversion  and  ruin  of  the 
system?  If,  for  instance,  the  result  of  this  mutual 
gravitation  should  be  to  increase  considerably  the  eccen- 
tricity of  the  earth's  orbit,  or  to  make  the  moon  approach 
continually  nearer  and  nearer  to  the  earth  at  every  revo- 
lution, it  is  easy  to  see  that  in  the  one  case,  our  year 
would  change  its  character,  producing  a  far  greater  ir- 
regularity in  the  distribution  of  the  solar  heat :  in  the 
other,  our  satellite  must  fall  to  the  earth,  occasioning  a 
dreadful  catastrophe.  If  the  positions  of  the  planetary 
orbits  with  respect  to  that  of  the  earth,  were  to  change 
much,  the  planets  might  sometimes  come  very  near  us, 
and  thus  increase  the  effect  of  their -attraction  beyond  cal«- 
culable  limits.  Under  such  circumstances  we  might  have 
years  of  unequal  length,  and  seasons  of  capricious  tem- 
perature ;  planets  and  moons  of  portentous  size  and  as- 
pect glaring  and  disappearing  at  uncertain  intervals ;  tides 
like  deluges  sweeping  over  whole  continents ;  and,  per- 
haps, the  collision  of  two  of  the  planets,  and  the  conse- 
quent destruction  of  all  organization  on  both  of  them. 
The  fact  really  is,  that  changes  are  taking  -place  in  the 
motions  of  the  heavenly  bodies,  which  have  gone  on 
progressively  from  the  first  dawn  of  .science.  The  ec- 
centricity of  the  earth's  orbit  has  been  diminishing  from 
the  earliest  observations  to  our  times.  The  moon  has 
been  moving  quicker  from  the  time  of  the  first  recorded 
eclipses,  and  is  now  in  advance  by  about  four  times  her 
own  breadth,  of  what  her  own  place  would  have  been  if 
it  had  not  been  affected  by  this  acceleration.  The  ob- 
liquity of  the  ecliptic  also,  is  in  a  state  of  diminution, 
and  is  now  about  two  fifths  of  a  degree  less  than  it  was 
in  the  time  of  Aristotle.  (Whewell,  in  the  Bridgewater 
Treatises,  p.  128.) 

275.  But  amid  so  many  seeming  causes  of  irregular- 
ity, and  ruin,  it  is  worthy  of  grateful  notice,  that  effec- 
tual provision  is  made  for  the  stability  of  the  solar  sys- 
tem. The  full  confirmation  of  this  fact,  is  among  the 
grand  results  of  Physical  Astronomy.  Newton  did  not 
undertake  to  demonstrate  either  the  stability  or  insta- 


STABILITY    OF    THE    SOLAR    SYSTEM.  217 

bility  of  the  system.  The  decision  of  this  point  re- 
quired a  great  number  of  preparatory  steps  and  simplifi- 
cations, and  such  progress  in  the  invention  and  improve- 
ment of  mathematical  methods,  as  occupied  the  best 
»nathematicians  of  Europe  for  the  greater  part  of  the 
ast  century.  Towards  the  end  of  that  time,  it  was 
'hown  by  La  Grange  and  La  Place,  that  the  arrange- 
ments of  the  solar  system  are  stable ;  that,  in  the 
iong  run,  the  orbits  and  motions  remain  unchanged; 
and  that  the  changes  in  the  orbits,  which- take  place  in 
shorter  periods,  never  transgress  certain  very  moderate 
limits.  Each  orbit  undergoes  deviations  on  this  side 
and  on  that  side  of  its  average  state ;  but  these  devia- 
tions are  never  very  great,  and  it  finally  recovers  from 
them,  so  that  the  average  is  preserved.  The  planets 
produce  perpetual  perturbations  in  each  other's  motions, 
but  these  perturbations  are  not  indefinitely  progressive, 
but  periodical,  reaching  a  maximum  value  and  then  di- 
minishing. The  periods  which  this  restoration  requires 
are  for  the  most  part  enormous, — not  less  than  thou- 
sands, and  in  some  instances  millions  of  years.  Indeed 
some  of  these  apparent  derangements,  have  been  going 
on  in  the  same  direction  from  the  creation  of  the  world. 
But  the  restoration  is  in  the  sequel  as  complete  as  the 
derangement ;  and  in  the  mean  time  the  disturbance 
never  attains  a  sufficient  amount  seriously  to  affect  the 
stability  of  the  system.  (Whewell,  in  the  Brid^ewater 
Treatises,  p.  128.)  I  have  succeeded  in  demonstrating 
(says  La  Place)  that,  whatever  be  the  masses  of  the  plan- 
ets, in  consequence  of  the  fact  that  they  all  move  in  the 
same  direction,  in  orbits  of  small  eccentricity,  and  but 
slightly  inclined  to  each  other,  their  secular  irregulari- 
ties are  periodical  and  included  within  narrow  limits ; 
so  that  the  planetary  system  will  only  oscillate  about  a 


275.  Is  the  system  stable  ?  Did  Newton  prove  this  ?  Who 
fully  established  this  point  ?  Have  all  the  inequalities  of  the 
planetary  motions  a  fixed  period  ?  How  long  are  some  of  these 
periods  ? 

19 


218  COMETS. 

mean  state,  and  will  never  deviate  from  it  except  by  3 
very  small  quantity.  The  ellipses  of  the  planets  have 
been  and  always  will  be  nearly  circular.  The  ecliptic 
will  never  coincide  with  the  equator ;  and  the  entire  ex- 
tent of  the  variation  in  its  inclination,  cannot  exceed 
three  degrees. 

276.  To  these  observations  of  La  Place,  Professor 
Whewell  adds  the  following  on  the  importance,  to  the 
stability  of  the  solar  system,  of  the  fact  that  those  plan- 
ets which  have  great  masses  have  orbits  of  small  eccen- 
tricity. The  planets  Mercury  and  Mars,  which  have 
much  the  largest  eccentricity  among  the  old  planets,  are 
those  of  which  the  masses  are  much  the  smallest.  The 
mass  of  Jupiter  is  more  than  two  thousand  times  that  of 
either  of  these  planets.  If  the  orbit  of  Jupiter  were  as 
eccentric  as  that  of  Mercury,  all  the  security  for  the  sta- 
bility of  the  system,  which  analysis  has  yet  pointed  out, 
would  disappear.  The  earth  and  the  smaller  planets 
might,  by  the  near  approach  of  Jupiter  at  his  perihelion, 
change  their  nearly  circular  orbits  into  very  long  ellipses, 
and  thus  might  fall  into  the  sun,  or  fly  off  into  remote 
space.  It  is  further  remarkable  that  in  the  newly  discov- 
ered planets,  of  which  the  orbits  are  still  more  eccentric 
than  that  of  Mercury,  the  masses  are  still  smaller,  so  that 
the  same  provision  is  established  in  this  case  also. 


CHAPTER  X. 

OF    COMETS. 


277.  A  COMET,  when  perfectly  formed,  consists  of 
three  parts,  the  Nucleus,  the  Envelope,  and  the  Tail. 
The  Nucleus,  or  body  of  the  comet,  is  generally  distin- 
guished by  its  forming  a  bright  point  in  the  center  of 
the  head,  conveying  the  idea  of  a  solid,  or  at  least  of  a 


276.  What  planets  have  orbits  of  small  eccentricity  ?     How 
does  this  fact  contribute  to  the  stability  of  the  system  ? 


COMETS.  219 

very  dense  portion  of  matter.  Though  it  is  usually  ex- 
ceedingly small  when  compared  with  the  other  parts  of 
the  comet,  yet  it  sometimes  subtends  an  angle  capable 
of  being  measured  by  the  telescope.  The  Envelope, 
(sometimes  called  the  coma)  is  a  dense  nebulous  cover- 
ing, which  frequently  renders  the  edge  of  the  nucleus 
so  indistinct,  that  it  is  extremely  difficult  to  ascertain  its 
diameter  with  any  degree  of  precision.  Many  comets 
have  no  nucleus,  but  present  only  a  nebulous  mass  ex- 
tremely attenuated  on  the  confines,  but  gradually  in- 
creasing in  density  towards  the  center.  Indeed  there  is 
a  regular  gradation  of  comets,  from  such  as  are  com- 
posed merely  of  a  gaseous  or  vapory  medium,  to  those 
which  have  a  well  defined  nucleus.  In  some  instances 
on  record,  astronomers  have  detected  with  their  tele- 
scopes small  stars  through  the  densest  part  of  a  comet. 
The  Tail  is  regarded  as  an  expansion  or  prolongation 
of  the  coma;* and,  presenting  as  it  sometimes  .does,  a 
train  of  appalling  magnitude,  and  of  a  pale,  disastrous 
light,  it  confers  on  this  class  of  bodies,  their  peculiar 
celebrity. 

Fig  48. 


These  several  parts  are  exhibited  in  figure  48,  which 
represents  the  appearance  of  the  comet  of  1680. 


277.  Of  what  three  parts  does  a  comet  consist  ?     Describe 
each. 


220  COMETS. 

278.  The  number  of  comets  belonging  to  the  solar 
system,  is  probably  very  great.  Many,  no  doubt,  escape 
observation  by  being  above  the  horizon  in  the  day  time. 
Seneca  mentions,  that  during  a  total  eclipse  of  the  sun, 
which  happened  60  years  before  the  Christian  era,  a 
large  and  splendid  comet  suddenly  made  its  appearance, 
being  very  near  the  sun.  The  elements  of  at  least  130 
have  been  computed,  and  arranged  in  a  table  for  future 
comparison.  Of  these  six  are  particularly  remarkable, 
viz.  the  comets,  of  1680,  1770,  and  1811;  and  those 
which  bear  the  names  of  Halley,  Biela,  and  Encke. 
The  comet  of  1680,  was  remarkable  not  only  for  its  as- 
tonishing size  and  splendor,  and  its  near  approach  to  the 
sun,  but  is  celebrated  for  having  submitted  itself  to  the 
observations  of  Sir  Isaac  Newton,  and  for  having  en- 
joyed the  signal  honor  of  being  the  first  comet  whose 
elements  were  determined  on  the  sure  basis  of  math- 
ematics. The  comet  of  1770,  is  memorable  for  the 
change's  its  orbit  has  undergone  by  the  action  of  Jupiter, 
as  will  be  more  particularly  related  in  the  sequel.  The 
comet  of  1811  was  the  most  remarkable  in  its  appear- 
ance of  all  that  have  been  seen  in  the  present  century. 
It  had  scarcely  any  perceptible  nucleus,  but  its  train 

Fig.  49. 


4  . 

was  very  long  and  broad,  as  is  represented  in  figure  49. 
Halley's  comet  (the  same  which  re-appeared  in  1835)  is 


COMETS  221 

distinguished  as  that  whose  return  was  first  successfully 
predicted,  and  whose  orbit  is  best  determined ;  and 
Biela's  and  Encke's  comets  are  well  known  for  their 
short  period^  of  revolution,  which  subject  them  fre- 
quently to  the  view  of  astronomers. 

279.  In  magnitude  and  brightness  comets  exhibit  a 
great  diversity.  History  informs  us  of  comets  so  bright 
as  to  be  distinctly  visible  in  the  day  time,  even  at  noon 
and  in  the  brightest  sunshine.  Such  was  the  comet 
seen  at  Rome  a  little  before  the  assassination  of  Julius 
Caesar.  The  comet  of  1680  covered  an  arc  of  the  heav- 
ens of  97°,  and  its  length  was  estimated  at  123,000,000 
miles.  That  of  1811,  had  a  nucleus  of  only  428  miles 
in  diameter,  but  a  tail  132,000,000  miles  long.  Had  it 
been  coiled  around  the  earth  like  a  serpent,  it  would 
have  reached  round  more  than  5,000  times.  Other  com- 
ets are  of  exceedingly  small  dimensions,  the  nucleus 
being  estimated  at  only  25  miles ;  and  some  which  are 
destitute  of  any  perceptible  nucleus,  appear  to  the  largest 
telescopes,  even  when  nearest  to  us,  only  as  a  small 
speck  of  fog,  or  as  a  tuft  of  down.  The  majority  of 
comets  can  be  seen  only  by  the  aid  of  the  telescope. 

The  same  comet,  indeed,  has  often  very  different  as- 
pects, at  its  different  returns.  Halley's  comet  in  1305 
was  described  by  the  historians  of  that  age,  as  the  comet 
of  terrific  magnitude  ;  (cometa  horrendce  magnitudinis ;) 
in  1456  its  tail  reached  from  the  horizon  to  the  zenith, 
and  inspired  such  terror,  that  by  a  decree  of  the  Pope  of 
Rome,  public  prayers  were  offered  up  at  noon-day  in  all 
the  Catholic  churches  to  deprecate  the  wrath  of  heaven, 
while  in  1682,  its  tail  was  only  30°  in  length,  and  in  1759 


278.  What  is  said  of  the  number  of  comets?     How  many 
have  been  arranged  in  a  table.    Specify  the  six  that  are  most 
remarkable.     State  particulars  respecting  each. 

279.  What  is  said  of  the  magnitude  and  brightness  of  com- 
ets ?     What  \vas  the  length  of  the  comet  of  1680  ?     Ditto  of 
1811  ?     Has  the  same  comet  different  aspects  at  different  re- 
turns ?     Example  in  Halley's  comet. 

19* 


222  COMETS. 

it  was  visible  only  to  the  telescope,  until  after  it  had  pas- 
sed the  perihelion.  At  its  recent  return  in  1835,  the 
greatest  length  of  the  tail  was  about  12°.  These  changes 
in  the  appearances  of  the  same  comet,  are  partly  owing 
to  the  different  positions  of  the  earth  wifh  respect  to 
them,  being  sometimes  much  nearer  to  them  when  they 
cross  its  track  than  at  others ;  also  one  spectator  so  situ- 
ated as  to  see  the  coma  at  a  higher  angle  of  elevation  or 
in  a  purer  sky  than  another,  will  see  the  train  longer  than 
it  appears  to  another  less  favorably  situated ;  but  the 
extent  of  the  changes  are  such  as  indicate  also  a  real 
change  in  magnitude  and  brightness. 

280.  The  periods  of  comets   in   their  revolutions 
around  the  sun,  are  equally  various.     Encke's  comet, 
which  has  the  shortest  known  period,  completes  its  rev- 
olution in  3^  years,  or  more  accurately,  in  1208  days  ; 
while  that  of  1811  is  estimated  to  have  a  period  of  3383 
years. 

281.  The  distances  to  which  different  comets  recede 
from  the  sun,  are  also  very  various.     While  Encke's 
comet  performs  its  entire  revolution  within  the  orbit  of 
Jupiter,  Halley's  comet  recedes  from  the  sun  to  twice 
the  distance  of  Uranus,  or  nearly  3600,000,000  miles. 
Some  comets,  indeed,  are   thought  to   go  to   a   much 
greater  distance  from  the  sun  than  this,  while  some  even 
are  supposed  to  pass  into  parabolic  or  hyperbolic  orbits, 
and  never  to  return. 

282.  Comets  shine  by  reflecting  the  light  of  the  sun. 
In  one  or  two  instances  they  have  exhibited  distinct 
phases,  although  the  nebulous  matter  with  which  the 
nucleus  is  surrounded,  would  commonly  prevent  such 


280.  How  arc  the  periods  of  comets  ?     What  is  that  of 
Encke's  comet,  and  that  of  the  comet  of  1811  ? 

281.  How  are  the  distances  of  comets  from  the  sun  ?    Coin- 
pare  Encke's  and  Halley's.  Do  comets  always  return  to  the  sun  ? 


COMETS.  223 

phases  from  being  distinctly  visible,  even  when  they 
would  otherwise  be  apparant.  Moreover,  certain  quali- 
ties of  polarized  light  enable  the  optician  to  decide 
whether  the  light  of  a  given  body  is  direct  or  reflected ; 
and  M.  Arago,  of  Paris,  by  experiments  of  this  kind  on 
the  light  of  the  comet  of  1819,  ascertained  it  to  be  re- 
flected light. 

283.  The  tail  of  a  comet  usually  increases  very  much 
as  it  approaches  the  sun ;  and  it  frequently  does  not  reach 
its  maximum  until  after  the  perihelion  passage.     In  re- 
ceding from  the  sun,  the  tail  again  contracts,  and  nearly 
or  quite  disappears  before  the  body  of  the  comet  is  en- 
tirely out  of  sight.     The  tail  is  frequently  divided  into 
two  portions,  the  central  parts,  in  the  direction  of  the 
axis,  being  less  bright   than  the   marginal   parts.     In 
1744,  a  comet  appeared  which  had  six  tails,  spread  out 
like  a  fan. 

The  tails  of  comets  extend  in  a  direct  line  from  the 
sun,  although  more  or  less  curved,  like  a  I  >ng  quill  or 
feather,  being  convex  on  the  side  next  to  the  direction 
in  which  they  are  moving  a  figure  which  may  result 
from  the  less  velocity  of  the  portions  most  remote  from 
the  sun.  Expansions  of  the  Envelope  have  also  been 
at  times  observed  on  the  side  next  the  sun,  but  these 
seldom  attain  any  considerable  length. 

284.  The  quantity  of  matter  in  comets  is  exceedingly 
small.     Their  tails  consist  of  matter  of  such  tenuity  that 
the  smallest  stars  are  visible  through  them.     They  can 
only  be  regarded  as  great  masses  of  thin  vapor,  suscepti- 
ble of  being  penetrated  through  their  whole  substance  by 


282.  Do  comets  shine  by  direct  or  by  reflected  light  ?    Do 
they  exhibit  phases  ?     How  is  it  known  that  their  light  is  re- 
flected and  not  direct  light ? 

283.  How  are  the  tails  of  comets  affected  by  being  near  the 
sun  ?  How  many  tails  have  some  comets  ?   In  what  direction 
is  the  tail  in  respect  to  the  snn  ? 


224  COMETS. 

the  sunbeams,  and  reflecting  them  alike  from  their  inte- 
rior parts  and  from  their  surfaces.  It  appears,  perhaps, 
incredible  that  so  thin  a  substance  should  be  visible  by 
reflected  light,  and  some  astronomers  have  held  that  the 
matter  of  comets  is  self-luminous ;  but  it  requires  but 
very  little  light  to  render  an  object  visible  in  the  night, 
and  a  light  vapor  may  be  visible  when  illuminated 
throughout  an  immense  stratum,  which  could  not  be 
seen  if  spread  over  the  face  of  the  sky  like  a  thin  cloud. 
From  the  extremely  small  quantity  of  matter  of  these 
bodies,  compared  with  the  vast  spaces  they  cover,  New- 
ton calculated  that  if  all  the  matter  constituting  the 
largest  tail  of  a  comet,  were  to  be  compressed  to  the 
same  density  with  atmospheric  air,  it  would  occupy  no 
more  than  a  cubic  inch.  This  is  incredible,  but  still 
the  highest  clouds  that  float  in  our  atmosphere,  must  be 
looked  upon  as  dense  and  massive  bodies,  compared  with 
the  filmy  and  all  but  spiritual  texture  of  a  comet. 

285.  The  small  quantity  of  matter  in  comets  is  proved 
by  the  fact,  that  they  have  sometimes  passed  very  near 
to  some  of  the  planets  without  disturbing  their  motions 
in  any  appreciable  degree.  Thus  the  comet  of  1770,  in 
its  way  to  the  sun,  got  entangled  among  the  satellites  of 
Jupiter,  and  remained  near  them  four  months,  yet  it  did 
not  perceptibly  change  their  motions.  The  same  comet 
also  came  veiy  near  the  earth ;  so  near,  that,  had  its 
mass  been  equal  to  that  of  the  earth,  it  would  have 
caused  the  earth  to  revolve  in  an  orbit  so  much  larger 
than  at  present,  as  to  have  increased  the  length  of  the 
year,  2h.  47rn.  Yet  it  produced  no  sensible  effect  on 
the  length  of  the  year,  and  therefore  its  mass,  as  is  shown 
by  La  Place,  "could  not  have  exceeded  y^V?  of  that  of 
the  earth,  and  might  have  been  less  than  this  to  any  ex- 


284.  How  is  the  quantity  of  matter  in  comets  ?  Of  what  do 
the  tails  consist  ?  Can  a  substance  so  thin  shine  by  reflected 
light  ?  What  opinion  had  Newton  of  the  extreme  tenuity  of 
the  material  of  comets'  tails  ? 


COMETS.  225 

tent.  It  may  indeed  be  asked,  what  proof  we  nave  that 
comets  have  any  matter,  and  are  not  mere  reflections  of 
light.  The  answer  is,  that,  although  they  are  not  able 
by  their  own  force  of  attraction  to  disturb  the  motions 
of  the  planets,  yet  they  are  themselves  exceedingly  dis- 
turbed by  the  action  of  the  planets,  and  in  exact  con- 
formity with  the  laws  of  universal  gravitation.  A  deli- 
cate compass  may  be  greatly  agitated  by  the  vicinity  of 
a  mass  of  iron,  while  the  iron  is  not  sensibly  affected  by 
the  attraction  of  the  needle. 

286.  By  approaching  very  near  to  a  large  planet,  a 
comet  may  have  its  orbit  entirely  changed.  This  fact 
is  strikingly  exemplified  in  the  history  of  the  comet  of 
1770.  At  its  appearance  in  1770,  its  orbit  was  found  to 
be  an  ellipse,  requiring  for  a  complete  revolution  only 
5|  years  ;  and  the  wonder  was,  that  it  had  not  been  seen 
before,  since  it  was  a  very  large  and  bright  comet.  As- 
tronomers suspected  that  its  path  had  been  changed,  and 
that  it  had  been  recently  compelled  to  move  in  this  short 
ellipse,  by  the  disturbing  force  of  Jupiter  and  his  satel- 
lites. The  French  Institute,  therefore,  offered  a  high 
prize  for  the  most  complete  investigation  of  the  elements 
of  this  comet,  taking  into  account  any  circumstances 
which  could  possibly  have  produced  an  alteration  in  its 
course.  By  tracing  back  the  movements  of  this  comet 
for  some  years  previous  to  1770,  it  was  found  that,  at 
the  beginning  of  1767,  it  had  entered  considerably  within 
the  sphere  of  Jupiter's  attraction.  Calculating  the  amount 
of  this  attraction  from  the  known  proximity  of  the  two 
bodies,  it  was  found  what  must  have  been  its  orbit  pre- 
vious to  the  time  when  it  became  subject  to  the  disturb- 
ing action  of  Jupiter.  The  result  showed  that  it  then 


285.  How  is  the  small  quantity  of  matter  in  comets  proved 
How  was  this  indicated  by  the  comet  of  1770  ?     What  did  its 
quantity  of  matter  not  exceed  as  compared  with  the  earth's  ? 
May  we  not  infer  that  they  have  no  matter  ? 


226  COMETS. 

moved  in  an  ellipse  of  greater  extent,  having  a  period  of 
50  years,  and  having  its  perihelion  instead  of  its  aphelion 
near  Jupiter.  It  was  therefore  evident  why,  as  long  as 
it  continued  to  circulate  in  an  orbit  so  far  from  the  cen- 
ter of  the  system,  it  was  never  visible  from  the  earth. 
In  January  1767,  Jupiter  and  the  comet  happened  to  be 
very  near  one  another,  and  as  both  were  moving  in  the 
same  direction,  and  nearly  in  the  same  plane,  they  re- 
mained in  the  neighborhood  of  each  other  for  several 
months,  the  planet  being  between  the  comet  and  the 
sun.  The  consequence  was,  that  the  comet's  orbit  was 
changed  into  a,  smaller  ellipse,  in  which  its  revolution 
was  accomplished  in  5£  years.  But  as  it  was  approach- 
ing the  sun  in  1779,  it  happened  again  to  fall  in  with 
Jupiter.  It  was  in  the  month  of  June,  that  the  attrac- 
tion of  the  planet  began  to  have  a  sensible  effect ;  and 
it  was  not  until  the  month  of  October  following,  that 
they  were  finally  separated. 

At  the  time  of  their  nearest  approach,  in  August,  Ju- 
piter was  distant  from  the  comet  only  T £T  of  its  distance 
from  the  sun,  and  exerted  an  attraction  upon  it  225 
times  greater  than  that  of  the  sun.  By  reason  of  this 
powerful  attraction,  Jupiter  being  farther  from  the  sun 
than  the  comet,  the  latter  was  drawn  out  into  a  new  or- 
bit, which  even  at  its  perihelion  came  no  nearer  to  the 
sun  than  the  planet  Ceres.  In  this  third  orbit,  the  comet 
requires  about  20  years  to  accomplish  its  revolution; 
and  being  at  so  great  a  distance  from  the  earth,  it  is  in- 
visible, and  will  forever  remain  so,  unless,  in  the  course 
of  ages,  it  may  undergo  new  perturbations,  and  move 
again  in  some  smaller  orbit  as  before. 


286.  How  may  a  comet  have  its  orbit  changed  ?  How  was 
the  orbit  of  the  comet  of  1770  changed?  How  was  this  fact  as- 
certained ?  What  action  did  Jupiter  exert  upon  it  in  1 767,  and 
again  in  1779  ?  How  far  was  Jupiter  from  the  comet  at -the 
time  of  their  nearest  approach  1  How  many  years  does  it  now 
require  to  perform  its  revolution  ? 


ORBITS    AND    MOTIONS    OF    COMETS.  227 


ORBITS    AND   MOTIONS    OP    COMETS. 

287.  The  planets,  as  we  have  seen,  (with  the  excep- 
tion of  the  four  new  ones,  which  seem  to  be  an  interme- 
diate class  of  bodies  between  planets  and  comets,)  move 
in  orbits  which  are  nearly  circular,  and  all  very  near  to 
the  plane  of  the  ecliptic,  and  all  move  in  the  same  direc- 
tion from  west  to  east.     But  the  orbits  of  comets  are  far 
more  eccentric  than  those  of  the  planets  ;  they  are  in- 
clined to  the  ecliptic  at  various  angles,  being  sometimes 
even  nearly  perpendicular  to  it ;   and  the  motions  of 
comets  are  sometimes  retrograde. 

288.  The  Elements  of  a  comet  are  five,  viz.  (1)  The 
perihelion  distance  ;  (2)  longitude  of  the  perihelion  ;  (3) 
longitude  of  the  node ;  (4)  inclination  of  the  orbit ;  (5) 
time  of  the  perihelion  passage. 

The  investigation  of  these  elements  is  a  problem  ex- 
tremely intricate,  requiring  for  its  solution,  a  skilful  and 
laborious  application  of  the  most  refined  analysis.  This 
difficulty  arises  from  several  circumstances  peculiar  to 
comets.  In  the  first  place,  from  the  elongated  form  of 
the  orbits  which  these  bodies  describe,  it  is  during  only 
a  very  small  portion  of  their  course,  that  they  are  visible 
from  the  earth,  and  the  observations  made  in  that  short 
period,  cannot  afterwards  be  verified  on  more  convenient 
occasions  ;  whereas  in  the  case  of  the  planets,  whose  or- 
bits are  nearly  circular,  and  whose  movements  may  be 
followed  uninterruptedly  throughout  a  complete  revolu- 
tion, no  such  impediments  to  the  determination  of  their 
orbits  occur.  In  the  second  place,  there  are  many  com- 
ets which  move  in  a  direction  opposite  to  the  order  of 
the  signs  in  the  zodiac,  and  sometimes  nearly  perpen- 
dicular to  the  plane  of  the  ecliptic  ;  so  that  their  appa- 


287.  How  do  the  orbits  of  comets  differ  from  those  of  planets  ? 

288.  What  particulars  are  called  the  elements  of  a  comet  ? 
What  is  said  of  the  difficulty  of  determining  these  elements  ? 
Specify  the  several  reasons  of  this  difficulty. 


COMETS. 


rent  course  through  the  heavens  is  rendered  extremely 
complicated,  on  account  of  the  contrary  motion  of  the 
earth.  In  the  third  place,  as  there  may  be  a  multitude 
of  elliptic  orbits,  whose  perihelion  distances  are  equal, 
(see  p.  100,)  it  is  obvious  that,  in  the  case  of  very  ec- 
centric orbits,  the  slightest  change  in  the  position  of  the 
curve  near  the  vertex,  where  alone  the  comet  can  be  ob- 
served, must  occasion  a  very  sensible  difference  in  the 
length  of  the  orbit ;  and  therefore,  though  a  small  error 
produces  no  perceptible  discrepancy  between  the  ob- 
served and  the  calculated  course,  while  the  comet  re- 
mains visible  from  the  earth,  its  effect  when  diffused 
over  the  whole  extent  of  the  orbit,  may  acquire  a  most 
material  or  even  a  fatal  importance. 

289.  On  account  of  these  circumstances,  it  is  found 
exceedingly  difficult  to  lay  down  the  path  which  a  comet 
actually  follows  through  the  whole  system,  and  least  of 
all,  possible  to  ascertain  with  accuracy,  the  length  of  the 
major  axis  of  the  ellipse,  and  consequently  the  periodical 
revolution.*  An  error  of  only  a  few  seconds  may  cause 
a  difference  of  many  hundred  years.  In  this  manner, 
though  Bessel  determined  the  revolution  of  the  comet  of 
1769  to  be  2089  years,  it  was  found  that  an  error  of  no 
more  than  5"  in  observation,  would  alter  the  period  either 
to  2678  years,  or  to  1692.  Some  astronomers,  in  calcula- 
ting the  orbit  of  the  great  comet  of  1680,  have  found  the 
length  of  its  greater  axis  426  times  the  earth's  distance 
from  the  sun,  and  consequently  its  period  8792  years ; 
whilst  others  estimate  the  greater  axis  430  times  the 
earth's  distance,  which  alters  the  period  to  8916  years. - 


289.  Is  it  easy  to  ascertain  the  major  axis  of  a  comet's  orbit, 
and  its  periodic  time  ?  What  difference  would  an  error  of  a  few 
seconds  occasion  ?  Give  examples  of  this. 


*  For  when  we  know  the  length  of  the  major  axis,  we  can  find  tht 
periodic  time  by  Kepler's  law,  which  applies  as  well  to  comets  as  t» 
planets. 


[OTIONS    AND    ORBITS    OF    COMETS. 


229 


Newton  and  Halley,  however,  judged  that  this  comet 
accomplished  its  revolution  in  only  570  years. 

290.  The  appearances  of  the  same  comet  at  different 
periods  of  its  return  are  so  various,  that  we  can  never 
pronounce  a  given  comet  to  be  the  same  with  one  that 
has  appeared  before,  from  any  peculiarities  in  its  physi- 
cal aspect.  The  identity  of  a  comet  with  one  already 
on  record,  is  determined  by  the  identity  of  the  elements. 
It  was  by  this  means  that  Halley  first  established  the 
identity  of  the  comet  which  bears  his  name,  with  one 
that  had  appeared  at  several  preceding  ages  of  the  world, 
of  which  so  many  particulars  were  left  on  record,  as  to 
enable  him  to  calculate  the  elements  at  each  period. 
These  were  as  in  the  following  table. 


Time  ot  appear. 

Inclin.  of  the  orbit. 

Lon.  of  Node. 

Lon.  of  Per. 

Per.  Dist. 

Course. 

1456 
1531 
1607 

1682 

17°  56' 
17    56 
17     02 
17    42 

48°   30' 
49     25 
50    21 

50    48 

30i°  00 
301     38 
302     16 
301     36 

0.58 
0.57 
0.58 
0.58 

Retrograde 

M 

(( 

On  comparing  these  elements,  no  doubt  could  be  en- 
tertained that  they  belonged  to  one  and  the  same  body ; 
and  since  the  interval  between  the  successive  returns 
was  seen  to  be  75  or  76  years,  Halley  ventured  to  pre- 
dict that  it  would  again  return  in  1758.  Accordingly, 
the  astronomers  who  lived  at  that  period,  looked  for  its 
return  with  the  greatest  interest.  It  was  found,  how- 
ever, that  on  its  way  towards  the  sun  it  would  pass  very 
near  to  Jupiter  and  Saturn,  and  by  their  action  on  it,  it 
would  be  retarded  for  a  long  time.  Clairaut,  a  distin- 
guished French  mathematician,  undertook  the  laborious 
task  of  estimating  the  exact  amount  of  this  retardation, 
and  found  it  to  be  no  less  than  618  days,  namely,  100 


290.  Can  we  identify  a  comet  with  one  that  has  been  seen 
before,  by  its  appearance  ?  How  is  this  identity  determined  ? 
How  was  Halley's  comet  proved  to  be  the  same  with  one  that 
had  appeared  before  ?  How  was  its  return  predicted  ?  What 
causes  alter  the  periods  of  its  return  ? 

20 


280  COMETS. 

days  by  the  action  of  Jupiter,  and  518  days  by  that  of 
Saturn,  This  would  delay  its  appearance  until  early  in 
the  year  1759,  and  Clairaut  fixed  its  arrival  at  the  peri- 
helion within  a  month  of  April  13th.  It  came  to  the 
perihelion  on  the  12th  of  March. 

291.  The   return   of  Halley's   comet   in    1835,  was 
looked  for  with  no  less  interest  than  in  1759.     Several 
of  the  most  accurate  mathematicians  of  that  age  had  cal- 
culated its  elements  with  inconceivable  labor.     Their 
zeal  was  rewarded  by  the  appearance  of  the  expected 
visitant  at  the  time  and  place  assigned ;  it  travelled  the 
northern  sky  presenting  the  very  appearances,  in  most 
respects,  that  had  been  anticipated  ;  and  came  to  its  pe- 
rihelion on  the  16th  of  November,  within  two  days  of 
the  time  predicted  by  Pontecoulant,  a  French  mathe- 
matician who  had,  it  appeared,  made  the  most  success- 
ful calculation.*     On  its  previous  return,  it  was  deemed 
an  extraordinary  achievement  to  have  brought  the  pre- 
diction within  a  month  of  the  actual  time. 

Many  circumstances  conspired  to  render  this  return  of 
Bailey's  comet  an  astronomical  event  of  transcendent 
interest.  Of  all  the  celestial  bodies',  its  history  was  the 
most  remarkable  ;  it  afforded  most  triumphant  evidence 
of  the  truth  of  the  doctrine  of  universal  gravitation,  and 
of  course  of  the  received  laws  of  astronomy ;  and  it  in- 
spired new  confidence  in  the  power  of  that  instrument, 
(the  Calculus,)  by  means  of  which  its  elements  had  been 
investigated. 

292.  Encke's  comet,  by  its  frequent  returns,  (once  in 
3£  years,)  affords  peculiar  facilities  for  ascertaining  the 


291  How  was  the  return  of  Halley's  comet  in  1835  re- 
garded by  astronomers  ?  What  circumstances  conspired  to 
produce  this  feeling  ? 

*  See  Professor  Loomis's  Observations  on  Halley's  Comet.  Amer. 
Jour.  Science,  30,  209. 


ORBITS    AND   MOTIONS    OF   COMETS.  231 

laws  of  its  revolution ;  and  it  has  kept  the  appointments 
made  for  it  with  great  exactness.  On  its  late  return 
(1839)  it  exhibited  to  the  telescope  a  globular  mass  of 
nebulous  matter,  resembling  fog,  and  moved  towards  its 
perihelion  with  great  rapidity. 

But  what  has  made.  Encke's  comet  particularly  fa- 
mous, is  its  having  first  revealed  to  us  the  existence  of  a 
Resisting  Medium  in  the  planetary  spaces.  It  has  long 
been  a  question,  whether  the  earth  and  planets  revolve 
in  a  perfect  void,  or  whether  a  fluid  of  extreme  rarity 
may  not  be  diffused  through  space.  A  perfect  vacuum 
was  deemed  most  probable,  because  no  such  effects  on 
the  motions  of  the  planets  could  be  detected  as  indicated 
that  they  encountered  a  resisting  medium.  But  a  feather 
or  a  lock  of  cotton  propelled  with  great  velocity,  might 
render  obvious  the  resistance  of  a  medium  which  would 
not  be  perceptible  in  the  motions  of  a  cannon  ball.  Ac- 
cordingly, Encke's  comet  is  thought  to  have  plainly  suf- 
fered a  retardation  from  encountering  a  resisting  medium 
in  the  planetary  regions.  The  effect  of  this  resistance, 
from  the  first  discovery  of  the  comet  to  the  present  time, 
has  been  to  diminish  the  time  of  its  revolution  about 
two  days.  Such  a  resistance  by  destroying  a  part  of  the 
projectile  force,  would  cause  the  comet  to  approach 
nearer  to  the  sun,  and  thus  to  have  its  periodic  time 
shortened.  The  ultimate  effect  of  this  cause  will  be  to 
bring  the  comet  nearer  to  the  sun  at  every  revolution, 
until  it  finally  falls  into  that  luminary,  although  many 
thousand  years  will  be  required  to  produce  this  catas- 
trophe. It  is  conceivable,  indeed,  that  the  effects  of 
such  a  resistance  may  be  counteracted  by  the  attraction 
of  one  or  more  of  the  planets,  near  which  it  may  pass  in 
its  successive  returns  to  the  sun. 


292.  Are  the  elements  of  Encke's  comet  calculated  with  ex- 
actness 1  What  was  its  appearance  in  1839  ?  What  has  made 
it  peculiarly  famous  ?  Why  should  it  be  so  favorable  for  detec- 
ting a  resisting  medium  ?  What  has  been  its  effect  on  the 
motions  of  the  comet  ?  What  will  be  its  ultimate  effect  ? 


232  COMETS. 

293.  It  is  peculiarly  interesting  to  see  a  portion  of 
matter,  of  a  tenuity  exceeding  the  thinnest  fog,  pursuing 
its  path  in  space,  in  obedience  to  the  same  laws  as  those 
which  regulate  such  large  and  heavy  bodies  as  Jupiter 
or  Saturn.     In  a  perfect  void,  a  speck  of  fog  if  propelled 
by  a  suitable  projectile  force,  would  revolve  around  the 
sun,  and  hold  on  its  way  through  the  widest  orbit,  with 
as  sure  and  steady  a  pace  as  the  heaviest  and  largest 
bodies  in  the  system. 

294.  Of  the  physical  nature  of  comets,  little  is  under- 
stood.    It  is  usual  to  account  for  the  variations  which 
their  tails  undergo,  by  referring  them  to  the  agencies  of 
heat  and  cold.     The  intense  heat  to  which  they  are 
subject  in  approaching  so  near  the  sun  as  some  of  them 
do,  is  alleged  as  a  sufficient  reason  for  the  great  expan- 
sion of  thin  nebulous  atmospheres  forming  their  tails ; 
and  the  inconceivable  cold  to  which  they  are  subject  in 
receding  to  such  a  distance  from  the  sun,  is  supposed  to 
account  for  the  condensation  of  the  same  matter  until  it 
returns  to  its  original  dimensions.     Thus  the  great  comet 
of  1680,  at  its  perihelion,  approached  166  times  nearer 
the  sun  than  the  earth,  being  only  130,000  miles  from 
the  surface  of  the  sun.     The  heat  which  it  must  have 
received,  was  estimated  to  be  equal  to  28,000  times  that 
which  the  earth  receives  in  the  same  time,  and  2000 
times  hotter  than  red  hot  iron.     This  temperature  would 
be  sufficient  to  volatilize  the  most  obdurate  substances, 
and  to  expand- the  vapor  to  vast  dimensions  ;  and  the  op- 
posite effects  of  the  extreme  cold  to  which  it  would  be 


293.  Does  the  extreme  tenuity  of  this  body  prevent  its  mov- 
ing in  obedience  to  the  laws  that  regulate  the  motions  of  the 
largest  bodies  in  the  system  ? 

294.  Is  the  physical  nature  of  comets  well  understood  ?  How 
are  the  variations  in  the  lengths  of  their  tails  accounted  for  ? 
How  near  did  the  comet  of  1680  approach  to  the  sun  ?     What 
heat  did  it  acquire  ?    Does  this  account  for  the  direction  of  tho 
tail  ?     How  is  that  accounted  for  by  some  writers  ? 


ORBITS    AND    MOTIONS    OF   COMETS.  233 

subject  in  the  regions  remote  from  the  sun,  would  be  ad- 
equate to  condense  it  into  its  former  volume. 

This  explanation,  however,  does  not  account  for  the 
direction  of  the  tail,  extending  as  it  usually  does,  only 
in  a  line  opposite  to  the  sun.  Some  writers  therefore, 
as  Delambre,  suppose  that  'the  nebulous  matter  of  the 
comet  after  being  expanded  to  such  a  volume,  that  the 
particles  are  no  longer  attracted  to  the  nucleus  unless  by 
the  slightest  conceivable  force,  are  carried  off*  in  a  direc- 
tion from  the  sun,  by  the  impulse  of  the  solar  rays  them- 
selves. But  to  assign  such  a  power  of  communicating 
motion  to  the  sun's  rays  while  they  have  never  been 
proved  to  have  any  momentum,  is  unphilosophical ;  and 
we  are  compelled  to  place  the  phenomena  of  comets' 
tails  among  the  points  of  astronomy  yet  to  be  explained. 

295.  Since  those  comets  which  have  their  perihelion 
very  near  the  sun,  like  the  comet  of  1680,  cross  the  or- 
bits of  all  the  planets,  the  possibility  that  one  of  them 
may  strike  the  earth,  has  frequently  been  suggested. 
Still  it  may  quiet  our  apprehensions  on  this  subject,  to 
reflect  on  the  vast  extent  of  the  planetary  spaces,  in 
which  these  bodies  are  not  crowded  together  as  we  see 
them  erroneously  represented  in  orreries  and  diagrams, 
but  are  sparsely  scattered  at  immense  distances  from 
each  other.  They  are  like  insects  flying  in  the  expanse 
of  heaven.  If  a  comet's  tail  lay  with  its  axis  in  the 
plane  of  the  ecliptic  when  it  was  near  the  sun,  we  can 
imagine  that  the  tail  might  sweep  over  the  earth ;  but 
the  tail  may  be  situated  at  any  angle  with  the  ecliptic 
as  well  as  in  the  same  plane  with  it,  and  the  chances 


295.  What  is  said  respecting  the  possibility  of  a  comet's  stri- 
king the  earth  ?  What  considerations  may  quiet  our  apprehen- 
sions ?  How  might  the  case  be  if  the  tail  lay  in  the  plane  of 
the  ecliptic  ?  Is  it  probable  that  a  comet  will  cross  the  ecliptic 
precisely  a^  the  place  of  the  earth's  path  ?  Have  comets  ac- 
tually approached  near  to  the  earth  ?  What  would  be  the  con- 
sequences were  a  comet  to  strike  the  earth  ? 


284  COMETS. 

that  it  will  not  be  in  the  same  plane,  are  almost  infinite. 
It  is  also  extremely  improbable  that  a  comet  will  cross 
the  plane  of  the  ecliptic  precisely  at  the  earth's  path  in 
that  plane,  since  it  may  as  probably  cross  it  at  any  other 
point,  nearer  or  more  remote  from  the  sun.  Still  some 
comets  have  occasionally  approached  near  to  the  earth. 
Thus  Biela's  comet  in  returning  to  the  sun  in  1832, 
crossed  the  ecliptic  very  near  to  the  earth's  track,  and 
had  the  earth  been  then  at  that  point  of  its  orbit,  it  might 
have  passed  through  a  portion  of  the  nebulous  atmos- 
phere of  the  comet.  The  earth  was  within  a  month  of 
reaching  that  point.  This  might  at  first  view  seem  to 
involve  some  nazard ;  yet  we  must  consider  that  a 
month  short,  implied  a  distance  of  nearly  50,000,000 
miles.  La  Place  has  assigned  the  consequences  that 
would  ensue  in  case  of  a  direct  collision  between  the 
earth  and  a  comet ;  but  terrible  as  he  has  represented 
them  on  the  supposition  that  the  nucleus  of  the  comet 
is  a  solid  body,  yet  considering  a  comet  (as  most  of  them 
doubtless  are)  as  a  mass  of  exceedingly  light  nebulous 
matter,  it  is  not  probable,  even  were  the  earth  to  make 
its  way  directly  through  a  comet,  that  a  particle  of  the 
comet  would  reach  the  earth.  The  portions  encountered 
by  the  earth,  would  be  arrested  by  the  atmosphere,  and 
probably  inflamed  ;  and  they  would  perhaps  exhibit,  on 
a  more  magnificent  scale  than  was  ever  before  observed, 
the  phenomena  of  shooting  stars,  or  meteoric  showers. 


PART   III. OF   THE    FIXED    STARS  AND  THE   SYS- 
TEM   OF    THE    WORLD. 


CHAPTER  I. 

OF   THE    FIXED    STARS CONSTELLATIONS. 

296.  THE  FIXED  STARS  are  so  called,  because,  to 
common  observation,  they  always  maintain  the  same 
situations  with  respect  to  one  another. 

The  stars  are  classed  by  their  apparent  magnitudes. 
The  whole  number  of  magnitudes  recorded  are  sixteen, 
of  which  the  first  six  only  are  visible  to  the  naked  eye  ; 
the  rest  are  telescopic  stars.  These  magnitudes  are  not 
determined  by  any  very  definite  scale,  but  are  merely 
ranked  according  to  their  relative  degrees  of  brightness, 
and  this  is  left  in  a  great  measure  to  the  decision  of  the 
eye  alone.  The  brightest  stars  to  the  number  of  15  or 
20,  are  considered  as  stars  of  the  first  magnitude  ;  the  50 
or  60  next  brightest,  of  the  second  magnitude  ;  the  next 
200  of  the  third  magnitude ;  and  thus  the  number  of 
each  class  increases  rapidly  as  we  descend  the  scale,  so 
that  no  less  than  fifteen  or  twenty  thousand  are  included 
within  the  first  seven  magnitudes. 

297.  The  stars  have  been  grouped  in  Constellations 
from  the  most  remote  antiquity ;  a  few,  as  Orion,  Bootes, 
and  Ursa  Major,  are  mentioned  in  the  most  ancient  wri- 
tings under  the  same  names  as  they  bear  at  present. 
The  names  of  the  constellations  are  sometimes  founded 


296.  Fixed  Stars. — Why  so  called  ?  How  classed  ?  Into 
how  many  magnitudes  are  they  divided  ?  How  many  are  there 
of  each  magnitude  ? 


236  FIXED    STARS. 

on  a  supposed  resemblance  to  the  objects  to  which  the 
names  belong ;  as  the  Swan  and  the  Scorpion  were  evi- 
dently so  denominated  from  their  likeness  to  those  ani- 
mals ;  but  in  most  cases  it  is  impossible  for  us  to  find 
any  reason  for  designating  a  constellation  by  the  figure 
of  the  animal  or  the  hero  which  is  employed  to  repre- 
sent it.  These  representations  were  probably  once 
blended  with  the  fables  of  pagan  mythology.  The 
same  figures,  absurd  as  they  appear,  are  still  retained  for 
the  convenience  of  reference ;  since  it  is  easy  to  find 
any  particular  star,  by  specifying  the  part  of  the  figure 
to  which  it  belongs,  as  when  we  say  a  star  is  in  the  neck 
of  Taurus,  in  the  knee  of  Hercules,  or  in  the  tail  of  the 
Great  Bear.  This  method  furnishes  a  general  clue  to 
its  position  ;  but  the  stars  belonging  to  any  constellation 
are  distinguished  according  to  their  apparent  magnitudes 
as  follows : — first,  by  the  Greek  letters,  Alpha,  Beta, 
Gamma,  &c.  Thus  Alpha  Orionis,  denotes  the  largest 
star  in  Orion ;  Beta  Andromeda,  the  second  star  in  An- 
dromeda ;  and  Gamma  Leonis,  the  third  brightest  star 
in  the  Lion.  Where  the  number  of  the  Greek  letters  is 
insufficient  to  include  all  the  stars  in  a  constellation, 
recourse  is  had  to  the  letters  of  the  Roman  alphabet,  a, 
b,  c,  &c.  ;  and,  in  cases  where  these  are  exhausted,  the 
final  resort  is  to  numbers.  This  is  evidently  necessary, 
since  the  largest  constellations  contain  many  hundrerds 
or  even  thousands  of  stars.  Catalogues  of  particular 
stars  have  also  been  published  by  different  astronomers, 
each  author  numbering  the  individual  stars  embraced  in 
his  list,  according  to  the  places  they  respectively  occupy 
in  the  catalogue.  These  references  to  particular  cata- 
logues are  sometimes  entered  on  large  celestial  globes. 
Thus  we  meet  with  a  star  marked  84  H.,  meaning  that 


297.  Constellations. — How  long  known  ?  Which  are  men- 
tioned in  the  most  ancient  writings  ?  How  far  are  the  names 
founded  on  resemblance  ?  Why  are  the  ancient  figures  still 
retained  ?  How  are  the  individual  stars  of  a  constellation  dis- 
tinguished ?  What  is  said  df  catalogues  of  the  stars  ? 


FIXED    STARS.  237 

this  is  its  number  in  Herschel's  catalogue  ;  or  140  M.,  de- 
noting the  place  the  star  occupies  in  the  catalogue  of 
Mayer. 

298.  The  earliest  catalogue  of  the  stars  was  made  by 
Hipparchus  of  the  Alexandrian  school,  about  140  years 
before  the  Christian  era.     A  new  star  appearing  in  the 
firmament,  he  was  induced  to  count  the  stars  and  to  re- 
cord their  positions,  in  order  that  posterity  might  be  able 
to  judge  of  the  permanency  of  the  constellations.     His 
catalogue   contains   all  that  were   conspicuous  to  the 
naked  eye  in  the  latitude  of  Alexandria,  being   1022. 
Most  persons  unacquainted  with  the  actual  number  of 
the  stars  which  compose  the  visible  firmament,  would 
suppose  it  to  be  much  greater  than  this ;  but  it  is  found 
that  the  catalogue  of  Hipparchus,  embraces  nearly  all 
that  can  now  be  seen  in  the  same  latitude,  and  that  on 
the  equator,  when  the  spectator  has  the  northern  and 
southern  hemispheres  both  in  view,  the  number  of  stars 
that  can  be  counted  does  not  exceed  3000.     A  careless 
view  of  the  firmament  in  a  clear  night,  gives  us  the  im- 
pression of  an  infinite  multitude  of  stSrs ;  but  when  we 
begin  to  count  them,  they  appear  much  more  sparsely 
distributed  than  we  supposed,  and  large  portions  of  the 
sky  appear  almost  destitute  of  stars. 

By  the  aid  of  the  telescope,  new  fields  of  stars  present 
themselves  of  boundless  extent ;  the  number  contin- 
ually augmenting  as  the  powers  of  the  telescope  are  in- 
creased. Lalande,  in  his  Histoire  Celeste,  has  registered 
the  positions  of  no  less  than  50,000  ;  and  the  whole 
number  visible  in  the  largest  telescopes  amounts  to  many 
millions. 

299.  It  is  strongly  recommended  to  the  learner  to  ac- 
quaint himself  with  the  leading  constellations  at  least, 


298.  Why  did  Hipparchus  make  a  catalogue  ?  How  many 
stars  did  he  number  ?  What  is  the  greatest  number  that  can 
be  seen  by  the  naked  eye  in  both  hemispheres  ?  How  many 
can  be  seen  by  the  telescope  ? 


238  FIXED    STARS. 

and  with  a  few  of  the  most  remarkable  individual  stars. 
The  task  of  learning  them  is  comparatively  easy,  and 
hardly  any  kind  of  knowledge,  attained  with  so  little 
labor,  so  amply  rewards  the  possessor.  It  will  generally 
be  advisable,  at  the  outset,  to  get  some  one  already  ac- 
quainted with  the  stars,  to  point  out  a  few  of  the  mo?, 
conspicuous  constellations,  those  of  the  Zodiac  for  ex» 
ample  ;  the  learner  may  then  resort  to  maps  of  the  stars, 
or  what  is  much  better,  to  a  celestial  globe,*  and  fill  up 
the  outline  by  tracing  out  the  principal  $tars  in  each 
constellation  as  there  laid  down.  By  adding  one  new 
constellation  to  his  list  every  night,  and  reviewing  those 
already  acquired,  he  will  soon  become  familiar  with  the 
stars,  and  will  greatly  augment  his  interest  and  improve 
his  intelligence  in  celestial  observations,  and  practical 
astronomy. 

CONSTELLATIONS. 

300.  We  will  point  out  particular  marks  by  which  the 
leading  constellations  may  be  recognized,  leaving  it  to 
the  learner,  after  he  has  found  a  constellation,  to  trace 
out  additional  members  of  it  by  the  aid  of  the  celestial 
globe,  or  by  maps  of  the  stars.  Let  us  begin  with  the 
Constellations  of  the  Zodiac,  which  succeeding  each 
other  as  they  do  in  a  known  order,  are  most  easily 
found. 

ARIES  (The  RAM)  is  a  small  constellation,  known  by 
two  bright  stars  which  form  his  head,  Alpha  and  Beta 
Arietis.  These  two  stars  are  four  degreesf  apart,  and 
directly  south  of  Beta  at  the  distance  of  one  degree,  is 


299.  Specify  the  directions  for  learning  the  constellations. 


*  For  the  method  of  rectifying  the  globe  so  as  to  represent  the  ap- 
pearance of  the  heavens  on  any  particular  evening,  see  page  34,  Art. 
61. 

t  These  measures  are  not  intended  to  be  stated  with  exactness,  but 
only  with  such  a  degree  of  accuracy  as  may  serve  for  a  general  guide. 


CONSTELLATIONS.  289 

a  smaller  star,  Gamma  Arietis.  It  has  been  already 
intimated  (Art.  139)  that  the  vernal  equinox  probably 
was  near  the  head  of  Aries,  when  the  signs  of  the  Zo- 
diac received  their  present  names. 

TAURUS  (The  BULL)  will  be  readily  found  by  the 
seven  stars  or  Pleiades,  which  lie  in  his  neck.  The 
largest  star  in  Taurus  is  Aldebaran,  in  the  Bull's  eye,  a 
star  of  the  first  magnitude,  of  a  reddish  color  somewhat 
resembling  the  planet  Mars.  Aldebaran  and  four  other 
stars  in  the  face  of  Taurus,  compose  the  Hyades. 

GEMINI  (The  TWINS)  is  known  by  two  very  bright 
stars,  Castor  and  Pollux,  four  degrees  asunder.  Castor 
(the  northern)  is  of  the  first,  and  Pollux  of  the  second 
magnitude. 

CANCER  (The  CRAB.)  There  are  no  large  stars  in  this 
constellation,  and  it  is  regarded  as  less  remarkable  than 
any  other  in  the  Zodiac.  It  contains  however  an  inter- 
esting group  of  small  stars,  called  Prcesepe  or  the  Neb- 
ula of  Cancer,  which  resembles  a  comet,  and  is  often 
mistaken  for  one,  by  persons  unacquainted  with  the 
stars.  With  a  telescope  of  very  moderate  powers  this 
nebula  is  converted  into  a  beautiful  assemblage  of  ex- 
ceedingly bright  stars. 

LEO  (The  LION)  is  a  very  large  constellation,  and  has 
many  interesting  members.  Regulus  (Alpha  Leonis) 
is  a  star  of  the  first  magnitude,  which  lies  directly  in  the 
ecliptic,  and  is  much  used  in  astronomical  observations. 


300.  Constellations  of  the  Zodiac. — Aries. — How  known  ? 
How  far  are  the  two  brightest  stars  apart  ?  Where  was  the 
vernal  equinox  situated  when  the  signs  of  the  Zodiac  received 
their  present  names  ? 

Taurus. — How  found  ?  Name  the  largest  star  in  Taurus. 
What  stars  compose  the  Hyades  ? 

Gemini. — How  known  1  How  far  are  Castor  and  Pollux 
asunder  ?  Of  what  magnitudes  are  they  respectively  ? 

Cancer. — Are  there  any  large  stars  in  Cancer  ?  What  is 
said  of  Praesepe  ? 

Leo. — What  is  its  size  ?  What  is  said  of  Regulus  ?  Where 
is  the  sickle  ?  Where  is  Denebola  situated  ? 


24r  FIXED    STARS. 

North  of  Regulus  lies  a  semi-circle  of  bright  stars,  form- 
ing a  sickle  of  which  Regulus  is  the  handle.  Denebola, 
a  star  of  the  second  magnitude,  is  in  the  Lion's  tail,  25° 
north  east  of  Regulus. 

VIRGO  (The  VIRGIN)  extends  a  considerable  way 
from  west  to  east,  but  contains  only  a  few  bright  stars. 
Spica,  however,  is  a  star  of  the  first  magnitude,  and 
lies  a  little  east  of  the  place  of  the  autumnal  equinox. 
Twenty-two  degrees  north  of  Spica,  is  Vindemiatrix,  in 
the  arm  of  Virgo,  a  star  of  the  third  magnitude. 

LIBRA  (The  BALANCE)  is  distinguished  by  three  large 
stars,  of  which  the  two  brightest  constitute  the  beam 
of  the  balance,  and  the  smallest  forms  the  top  or  handle. 

SCORPIO  (The  SCORPION)  is  one  of  the  finest  of  the 
constellations.  His  head  is  formed  of  five  bright  stars 
arranged  in  the  arc  of  a  circle,  which  is  crossed  in  the 
center  by  the  ecliptic  nearly  at  right  angles,  near  the 
brightest  of  the  five,  Beta  Scorpionis.  Nine  degrees 
southeast  of  this,  is  a  remarkable  star  of  the  first  mag- 
nitude, of  a  reddish  color,  called  Cor  Scorpionis,  or  An- 
tares.  South  of  this  a  succession  of  bright  stars  sweep 
round  towards  the  east,  terminating  in  several  small 
stars,  forming  the  tail  of  the  Scorpion. 

SAGITTARIUS  (The  ARCHER.)  Northeast  of  the  tail  of 
the  Scorpion,  are  three  stars  in  the  arc  of  a  circle  which 
constitute  the  bow  of  the  Archer,  the  central  star  being 
the  brightest,  directly  west  of  which  is  a  bright  star 
which  forms  the  arrow. 

CAPRICORNUS  (The  GOAT)  lies  northeast  of  Sagittarius, 
and  is  known  by  two  bright  stars,  three  degrees  apart, 
which  form  the  head. 


Virgo. — Extent  from  east  to  west  ?  What  is  said  of  Spica, 
and  of  Vindemiatrix  ? 

Libra. — How  distinguished  ? 

Scorpio. — His  appearance  ?  His  head  how  formed  ?  Where 
is  Antares  situated  ? 

Sagittarius. — Describe  his  bow. 

Capricornus. — Where  situated  from  Sagittarius  ?  How 
known  ? 


CONSTELLATIONS.  241 

AQUARIUS  (The  WATER  BEARER)  is  recognized  by 
two  stars  in  a  line  with  Alpha  Capricorni,  forming  the 
shoulders  of  the  figure.  These  two  stars  are  10°  apart, 
and  4°  southeast  is  a  third  star,  which,  together  with  the 
other  two,  makes  an  acute  triangle,  of  which  the  west- 
ernmost is  the  vertex. 

PISCES  (The  FISHES)  lie  between  Aquarius  and  Aries. 
They  are  not  distinguished  by  any  large  stars,  but  are 
connected  by  a  series  of  small  stars,  that  form  a  crooked 
line  between  them.  Piscis  Australis,  the  Southern 
Fish,  lies  directly  below  Aquarius,  and  is  known  by  a 
single  bright  star  far  in  the  south,  having  a  declination 
of  30°.  The  name  of  this  star  is  Fomalhaut,  and  it  is 
much  used  in  astronomical  measurements. 

301.  The  Constellations  of  the  Zodiac,  being  first 
well  learned,  so  as  to  be  easily  recognized,  will  facil- 
itate the  learning  of  others  that  lie  north  and  south  of 
them.  Let  us  therefore  next  review  the  principal  North- 
ern Constellations,  beginning  north  of  Aries  and  pro- 
ceeding from  west  to  east. 

ANDROMEDA,  is  characterized  by  three  stars  of  the  sec- 
ond magnitude,  situated  in  a  straight  line,  extending 
from  west  to  east.  The  middle  star  is  about  17°  north 
of  Beta  Arietis.  It  is  in  the  girdle  of  Andromeda,  and 
is  named  Mirach.  The  other  two  lie  at  about  equal 
distances,  14°  west  and  east  of  Mirach.  The  western 
star,  in  the  head  of  Andromeda,  lies  in  the  Equinoctial 
Colure.  The  eastern  star,  Alamak,  is  situated  in  the 
foot. 

PERSEUS  lies  directly  north  of  the  Pleiades,  and  con- 
tains several  bright  stars.  About  18°  from  the  Pleiades 


Aquarius. — How  recognized  ?  How  far  apart  are  the  shoul- 
ders of  Aquarius  ? 

Pisces. — Where  situated  ?  How  connected  ?  Where  is 
Piscis  Australis  situated  ?  By  what  name  is  it  commonly 
known  ? 

301  Northern  Constellations.  Andromeda,  how  character- 
ized ?  Where  are  Mirach  and  Alamak  situated  ? 

21 


242  FIXED    STARS. 

is  Algol,  a  star  of  the  second  magnitude  in  the  Head  of 
Medusa,  which  forms  a  part  of  the  figure  ;  and  9°  north- 
east of  Algol  is  Algenib,  of  the  same  magnitude  in  the 
back  of  Perseus.  Between  Algenib  and  the  Pleiades  are 
three  bright  stars,  at  nearly  equal  intervals,  which  com- 
pose the  right  leg  of  Perseus. 

AURIGA  (the  WAGONER)  lies  directly  east  of  Perseus, 
and  extends  nearly  parallel  to  that  constellation  from 
north  to  south.  Capella  a  very  white  and  beautiful 
star  of  the  first  magnitude,  distinguishes  this  constella- 
tion. The  feet  of  Auriga  are  near  the  Bull's  Horns. 

The  LYNX  comes  next,  but  presents  nothing  particu- 
larly interesting,  containing  no  stars  above  the  fourth 
magnitude. 

LEO  MINOR  consists  of  a  collection  of  small  stars 
north  of  the  sickle  in  Leo,  and  south  of  the  Great  Bear. 
Its  largest  star  is  only  of  the  third  magnitude. 

COMA  BERENICES  is  a  cluster  of  small  stars,  north  of 
Denebola,  (a  star  in  the  tail  of  the  Lion,)  and  of  the  head  of 
Virgo.  About  12°  north  of  Berenice's  Hair,  is  a  single 
bright  star  called  Cor  Caroli,  or  Charles's  Heart. 

BOOTES,  which  comes  next,  is  easily  found  by  means 
of  Arcturus,  a  star  of  the  first  magnitude,  of  a  reddish 
color,  which  is  situated  near  the  knee  of  the  figure. 
Arcturus  is  accompanied  by  three  small  stars  forming  a 
triangle  a  little  to  the  southwest.  Two  bright  stars 
Gamma  and  Delta  Bootis,  form  the  shoulders,  and 
Beta  of  the  third  magnitude  is  in  the  head  of  the 
figure. 

CORONA  BOREALIS,  (The  CROWN>)  which  is  situated  east 


Perseus. — How  situated  with  respect  to  the  Pleiades  ? 
Where  is  Algol  ?  Where  is  Algenib  1  What  stars  compose 
the  right  leg  of  Perseus  ? 

Auriga. — How  situated  from  Perseus  ?  What  large  star  dis- 
tinguishes this  constellation  ?  Where  are  the  feet  of  Auriga  ? 

Lynx. — Size  of  its  stars  ? 

Leo  Minor. — Where  situated  ?     Size  of  its  largest  star  ? 

Coma  Berenices. — Describe  it.     Where  is  Cor  Caroli  ? 

Bootes. — What  large  star  is  in  this  constellation  ? 


UNIVERSITY 

OF 

t Q Kl\ ^ 

of  Bootes,  is  very  easily  recognized,  composed  as  it  is  of 
a  semi-circle  of  bright  stars.  In  the  center  of  the  bright 
crown,  is  a  star  of  the  second  magnitude,  called  Gem- 
ma ;  the  remaining  stars  are  all  much  smaller. 

HERCULES,  lying  between  the  Crown  on  the  west  and 
the  Lyre  on  the  east,  is  very  thick  set  with  stars,  most 
of  which  are  quite  small.  The  Constellation  covers  a 
great  extent  of  the  sky,  especially  from  N.  to  S.,  the 
head  terminating  within  15°  of  the  equator,  and  marked 
by  a  star  of  the  third  magnitude,  called  Ras  Algethi, 
which  is  the  largest  in  the  Constellation. 

OPHIUCUS  js  situated  directly  south  of  Hercules,  ex- 
tending some  distance  on  both  sides  of  the  equator,  the 
feet  resting  on  the  Scorpion.  The  head  terminates  near 
the  head  of  Hercules,  and  like  that,  is  marked  by  a 
bright  star  within  5°  of  Alpha  Herculis.  Ophiucus  is 
represented  as  holding  in  his  hands  the  SERPENT,  the 
head  of  which,  consisting  of  three  bright  stars,  is  sit- 
uated a  little  south  of  the  Crown.  The  folds  of  the 
serpent  will  be  easily  followed  by  a  succession  of  bright 
stars  which  extend  a  great  way  to  the  east. 

AQTJILA  (The  EAGLE)  is  conspicuous  for  three  bright 
stars  in  its  neck,  of  which  the  central  one,  Altair,  is  a 
very  brilliant  white  star  of  the  first  magnitude.  Anti- 
nous  lies  directly  south  of  the  Eagle,  and  north  of  the 
head  of  Capricornus. 

DELPHINUS  (The  DOLPHIN)  is  a  small  but  beautiful 
Constellation,  a  few  degrees  east  of  the  Eagle,  and  is 
characterized  by  four  bright  stars  near  to  one  another, 
forming  a  small  rhombic  square.  Another  star  of  the 
same  magnitude  5°  south,  makes  the  tail. 


Corona  Borealis. — Describe  it.    Where  is  Gemma  situated  ? 

Hercules. — Between  what  two  constellations  is  it  ?  What 
is  said  of  its  extent  ?  Where  is  Ras  Algethi  ? 

Ophiucus. — Where  is  it  from  Hercules  ?  How  is  it  repre- 
sented ? 

Aquila. — How  distinguished  ?  Where  is  Altair  1  Where  is 
Ajitinous  ? 

The  Dolphin- — Describe  it. 


244  FIXED    STARS, 

PEGASUS  lies  between  Aquarius  on  the  southwest  arid 
Andromeda  on  the  northeast.  It  contains  but  few  large 
stars.  A  very  regular  square  of  bright  stars  is  composed 
of  Alpha  Andromeda,  and  the  three  largest  stars  in  Pe- 
gasus, namely,  Sckeat,  Markab,  and  Algenib.  The 
sides  composing  this  square  are  each  about  15°.  Alge- 
nib is  situated  in  the  Equinoctial  Colure. 

302.  We  may  now  review  the  Constellations  which 
surround  the  North  Pole,  within  the  circle  of  perpetual 
apparition.  (Art.  38.) 

URSA  MINOR  (The  LITTLE  BEAR)  lies  nearest  the 
pole.  The  Pole-star,  Polaris,  is  in  the  extremity  of  the 
tail,  and  is  of  the  third  magnitude.  Three  stars  in  a 
straight  line  4°  or  5°  apart,  commencing  with  the  Pole- 
star,  lead  to  a  trapezium  of  four  stars,  and  the  whole 
seven  form  together  a  dipper,  the  trapezium  being  the 
body,  and  the  three  stars  the  handle. 

URSA  MAJOR  (The  GREAT  BEAR)  is  situated  between 
the  pole  and  the  Lesser  Lion,  and  is  usually  recognized 
by  the  figure  of  a  larger  and  more  perfect  dipper,  which 
constitutes  the  hinder  part  of  the  animal.  This  has  also 
seven  stars,  four  in  the  body  of  the  dipper,  and  three  in 
the  handle.  All  these  are  stars  of  much  celebrity  The 
two  in  the  western  SKJ£  of  the  dipper,  Alpha  and  Beta,  are 
called  Pointers,  on  account  of  their  always  being  in  a 
right  line  with  the  Pole-star,  and  therefore  affording  an 
easy  mode  of  finding  that.  The  first  star  in  the  tail,  next 
the  body,  is  named  Alioth,  and  the  second  Mizar.  The 
head  of  the  Great  Bear  lies  far  to  the  westward  of  the 


Pegasus.  —  Between  what  two  constellations  is  it  situated? 
How  may  a  square  be  formed  of  certain  stars  in  this  constel- 
lation ? 

302.  Northern  Constellations.  Ursa  Minor. — How  situated 
with  respect  to  the  pole  ?  Show  how  the  dipper  in  this  con- 
stellation is  formed  ? 

Ursa.  Major. — Where  situated  ?  How  recognized  ?  What 
are  the  Pointers  ?  Where  is  Alioth — Mizar  ?  Of  what  is  the 
head  composed  ? 


CONSTELLATIONS.  24 

Pointers,  and  is  composed  of  numerous  small  stars ;  and 
the  feet  are  severally  composed  of  two  small  stars  very 
near  to  each  other. 

DRACO  (The  DRAGON)  winds  round  between  the  Great 
and  the  Little  Bear ;  and  commencing  with  the  tail,  be- 
tween the  Pointers  and  the  Pole-star,  it  is  easily  traced 
by  a  succession  of  bright  stars  extending  from  west  to 
east,  passing  under  Ursa  Minor,  it  returns  westward,  and 
terminates  in  a  triangle  which  forms  the  head  of  Draco, 
near  the  feet  of  Hercules,  northwest  of  Lyra. 

CEPHEUS  lies  eastward  of  the  breast  of  the  Dragon, 
but  has  no  stars  above  the  third  magnitude. 

CASSIOPEIA  is  known  by  the  figure  of  a  chair,  com- 
posed of  four  stars  which  form  the  legs,  and  two  which 
form  the  back.  This  constellation  lies  between  Perseus 
and  Cepheus,  in  the  Milky  Way. 

CYGNUS  (The  SWAN)  is  situated  also  in  the  Milky  Way, 
some  distance  southwest  of  Cassiopeia,  towards  the  Ea- 

f1  5.  Three  bright  stars,  which  lie  along  the  Milky 
ay,  form  the  body  and  neck  of  the  Swan,  and  two 
others  in  a  line  with  the  middle  one  of  the  three,  one 
above  and  one  below,  constitute  the  wings.  This  Con- 
stellation is  among  the  few,  that  exhibit  some  resem- 
blance to  the  animals  whose  names  they  bear. 

LYRA  (The  LYRE)  is  directly  west  of  the  Swan,  and 
is  easily  distinguished  by  a  beautiful  white  star  of  the 
first  magnitude,  Alpha  Lyrce. 

303.  The  Southern  Constellations  are  comparatively 
few  in  number.  We  shall  notice  only  the  Whale,  Orion, 
the  Greater  and  Lesser  Dog,  Hydra,  and  the  Crow. 


Draco. — How  situated   with  respect  to  the  two   Bears  ? 
Trace  its  course  ? 

Cepheus. — How  situated  from  Draco  ? 

Cassiopeia. — How  known  ?     Where  situated  ? 

Cygnus. — How  situated  1    Of  what  stars  formed  ?    Has  this 
constellation  any  resemblance  to  a  Swan  ? 

303.  Southern  Constellations.     Cetus. — Its  extent  ?     Size 
of  its  stars  ?     What  is  said  of  Menkar,  and  of  Mira  ? 
21* 


246  FIXED    STARS. 

CETUS  (The  WHALE)  is  distinguished  rather  for  its 
extent  than  its  brilliancy,  reaching  as  it  does  through 
40°  of  longitude,  while  none  of  its  stars  except  one, 
are  above  the  third  magnitude.  Menkar  (Alpha  Ceti) 
in  the  mouth,  is  a  star  of  the  second  magnitude,  and 
several  other  bright  stars  directly  south  of  Aries,  make 
the  head  and  neck  of  the  Whale.  Mira  (Omicron 
Ceti)  in  the  neck  of  the  Whale  is  a  variable  star. 

ORION  is  one  of  the  largest  and  most  beautiful  of  the 
constellations,  lying  southeast  of  Taurus.  A  cluster  of 
small  stars  form  the  head  ;  two  large  stars,  Betalgeus  of 
the  first  and  Bellatrix  of  the  second  magnitude,  make 
the  shoulders ;  three  more  bright  stars  compose  the 
buckler,  and  three  the  sword ;  and  Rigel,  another  star  of 
the  first  magnitude,  makes  one  of  the  feet.  In  this 
Constellation  there  are  70  stars  plainly  visible  to  the 
naked  eye,  including  two  of  the  first  magnitude,  four  of 
the  second,  and  three  of  the  third. 

CANIS  MAJOR  lies  S.  E.  of  Orion,  and  is  distinguished 
chiefly  by  its  containing  the  largest  of  the  fixed  stars, 
Siriug. 

CANIS  MINOR  a  little  north  of  the  equator,  between 
Canis  Major  and  Gemini,  is  a  small  Constellation,  con- 
sisting chiefly  of  two  stars,  of  which  Procyon  is  of  the 
first  magnitude. 

HYDRA  has  its  head  near  Procyon,  consisting  of  a 
number  of  stars  of  ordinary  brightness.  About  17°  S. 
E.  of  the  head,  is  a  star  of  the  second  magnitude,  form- 
ing the  heart,  (Cor  Hydrce ;)  and  eastward  of  this,  is 
a  long  succession  of  stars  of  the  fourth  and  fifth  magni- 
tudes composing  the  body  and  the  tail,  and  reaching  a 
few  degrees  south  of  Spica  Virginis. 

Orion. — What  is  said  of  its  size  and  beauty  ?  Describe  its 
different  parts.  How  many  stars  does  it  contain  which  are 
visible  to  the  naked  eye  ? 

Canis  Major. — Where  situated  -from  Orion  ?  What  large 
star  is  in  it  ? 

Cams  Minor. — Where  situated  ?  What  large  star  does  it 
contain  ? 

Hydra. — Trace  its  course. 


CLUSTERS    OF   STARS.  247 

CORVUS  (The  CROW)  is  represented  as  standing  on  the 
tail  of  Hydra.  It  consists  of  small  stars,  onlv  three  of 
which  are  as  large  as  the  third  magnitude. 

304.  The  foregoing  brief  sketch  is  designed  merely 
to  aid  the  student  in  finding  the  principal  constellations 
and  the  largest  fixed  stars.  When  we  have  once  learned 
to  recognize  a  constellation  by  some  characteristic  marks, 
we  may  afterwards  fill  up  the  outline  by  the  aid  of  a 
celestial  globe  or  a  map  of  the  stars.  It  will  be  of  little 
avail  however,  merely  to  commit  this  sketch  to  memory ; 
but  it  will  be  very  useful  for  the  student  at  once  to  ren- 
der himself  familiar  with  it,  from  the  actual  specimens 
which  every  clear  evening  presents  to  his  view. 


CHAPTER    II. 

VF  CLUSTERS  OF  STARS NEBULA VARIABLE  STARS — 

TEMPORARY  STARS DOUBLE  STARS. 

305.  IN  various  parts  of  the  firmament  are  seen  large 
groups  or  clusters,  which,  either  by  the  naked  eye,  or  by 
the  aid  of  the  smallest  telescope,  are  perceived  to  con- 
sist of  a  great  number  of  small  stars.  Such  are  the 
Pleiades,  Coma  Berenices,  and  Prsesepe  or  the  Bee-hive 
in  Cancer.  The  Pleiades,  or  Seven  stars,  as  they  are 
called,  in  the  neck  of  Taurus,  is  the  most  conspicuous 
cluster.  When  we  look  directly  at  this  group,  we  can. 
not  distinguish  more  than  six  stars,  but  by  turning  the 
eye  sideways*  upon  it,  we  discover  that  there  are  many 


Corvus. — How  represented  ? 

305.  Clusters. — Name  a  few  of  the  largest.  Pleiades, 
where  situated  ?  How  many  stars  does  it  contain  ?  What 
is  said  of  Coma  Berenices,  and  of  the  Bee-hive  ? 

*  Indirect  vision  is  far  more  delicate  than  direct.  Thus  we  can  see 
the  Zodiacal  Light  or  a  Comet's  Tail,  much  more  distinctly  and  better 
denned,  if  we  fix  one  eye  on  a  part  of  the  heavens  at  some  distance,  and 
turn  the  other  eye  obliquely  upon  the  object. 


248  FIXED    STARS. 

more.  Telescopes  show  50  or  60  stars  crowded  to* 
gether  and  apparently  insulated  from  the  other  parts  of 
the  heavens.  Coma  Berenices  has  fewer  stars,  but  they 
are  of  a  larger  class  than  those  which  compose  the  Plei- 
ades. The  Bee-hive  or  Nebula  of  Cancer  as  it  is  called, 
is  one  of  the  finest  objects  of  this  kind  for  a  small  tel- 
escope, being  by  its  aid  converted  into  a  rich  congeries 
of  shining  points.  The  head  of  Orion  affords  an  exam- 
ple of  another  cluster,  though  less  remarkable  than  the 
others. 

306.  Nebulce  are  those  faint  misty  appearances  which 
resemble  comets,  or  a  small  speck  of  fog.  The  Galaxy 
or  Milky  Way,  presents  a  continued  succession  of  large 
nebulae.  A  very  remarkable  Nebula,  visible  to  the  naked 
eye,  is  seen  in  the  girdle  of  Andromeda.  No  powers  of 
the  telescope  have  been  able  to  resolve  this  into  separate 
stars.  Its  dimensions  are  astonishingly  great.  In  diam- 
eter it  is  about  15'.  The  telescope  reveals  to  us  innumer- 
able objects  of  this  kind.  Sir  William  Herschel  has  given 
catalogues  of  2000  Nebulae,  and  has  shown  that  the  neb- 
ulous matter  is  distributed  through  the  immensity  of 
space  in  quantities  inconveivably  great,  and  in  separate 
parcels  of  all  shapes  and  sizes,  and  of  all  degrees  of 
brightness  between  a  mere  milky  appearance  and  the 
condensed  light  of  a  fixed  star.  Finding  that  the  gra- 
dations between  the  two  extremes  were  tolerably  regu- 
lar, he  thought  it  probable  that  the  nebulae  form  the  ma- 
terials out  of  which  nature  elaborates  suns  and  systems  ; 
and  he  conceived  that,  in  virtue  of  a  central  gravitation, 
each  parcel  of  nebulous  matter  becomes  more  and  more 
condensed,  and  assumes  a  rounded  form.  He  inferred 
from  the  eccentricity  of  its  shape,  and  the  effects  of  the 
mutual  gravitation  of  its  particles,  that  it  acquires  gradu- 


306.  Nebula. — What  are  they  ?    What  is  said  of  the  nebula 
in  the  girdle  of  Andromeda  ?     How  many  nebulae  has  Sir  W. 
Herschel  included  in  his  catalogue  1     What  are  his  ideas  re 
specting  nebulae  ? 


NEKUL.E.  249 

ally  a  rotary  motion  ;  that  the  condensation  goes  on  in 
creasing  until  the  mass  acquires  consistency  and  solidity 
and  all  the  characters  of  a  comet  or  a  planet ;  that  by  a 
still  further  process  of  condensation,  the  body  becomes  a 
real  star,  self-shining ;  and  that  thus  the  waste  of  the  ce- 
lestial bodies,  by  the  perpetual  diffusion  of  their  light,  is 
continually  compensated  and  restored  by  new  formations 
of  such  bodies,  to  replenish  forever  the  universe  with 
planets  and  stars. 

307.  These  opinions  are  recited  here  rather  out  of  re- 
spect to  their  notoriety  and  celebrity,  than  because  we 
suppose  them  to  be  founded  on  any  better  evidence  than 
conjecture.  The  Philosophical  Transactions  for  many 
years,  both  before  and  after  the  commencement  of  the 
present  century,  abound  with  both  the  observations  and 
speculations  of  Sir  William  Herschel.  The  former  are 
deserving  of  all  praise ;  the  latter  of  much  less  confi- 
dence. Changes,  however,  are  going  on  in  some  of  the 
nebulae,  which  plainly  show  that  they  are  not,  like  plan- 
ets and  stars,  fixed  and  permanent  creations.  Thus  the 
great  nebula  in  the  girdle  of  Andromeda,  has  very  much 
altered  its  structure  since  it  first  became  an  object  of  tele- 
scopic observation.  Many  of  the  nebulae  are  of  a  globu- 
lar form,  (Fig.  50,)  but  frequently  they  present  the  ap- 
pearance of  a  rapid  increase  of  numbers  towards  the  cen- 
(Fiff.  50.)  (Fig.  51.) 


ter,  (Fig.  51,)   the   anterior  boundary  being  irregular, 
and  the  central  parts  more  nearly  spherical. 


307.  What  is  said  of  Herschel's  speculations  and  of  his  ob- 
servations 1  What  changes  occur  in  the  nebulae  ?  What 
forms  have  they  ? 


250  FIXED    STARS. 

308.  The  nebula  in  the  sword  of  Orion  is  particularly 
celebrated,  being  very  large  and  of  a  peculiarly  interest- 
ing appearance.     According  to  Sir  John  Herschel,  its 
nebulous  character  is  very  different  from  what  might  be 
supposed  to  arise  from  the  assemblage  of  an  immense 
collection  of  small  stars.     It  is  formed  of  little  flocculent 
masses  like  wisps  of  clouds ;  and  such  wisps  seem  to 
adhere  to  many  small  stars  at  its  outskirts,  and  especially 
to  one  considerable  star  which  it  envelops  with  a  neb- 
ulous atmosphere  of  considerable  extent  and  singular 
figure. 

Descriptions,  however,  can  convey  but  a  very  imper- 
fect idea  of  this  wonderful  class  of  astronomical  objects, 
and  we  would  therefore  urge  the  learner  studiously  to 
avail  himself  of  the  first  opportunity  he  may  have  to 
view  them  through  a  large  telescope,  especially  the  Neb- 
ula of  Andromeda  and  of  Orion. 

309.  Nebulous  Stars  are  such  as  exhibit  a  sharp  and 
brilliant  star  surrounded  by  a  disk  or  atmosphere  of  neb- 
ulous matter.     These  atmospheres  in  some  cases  present 
a  circular,  in  others  an  oval  figure  ;   and  in  some  in- 
stances, the  nebula  consists  of  a  long,  narrow  spindle- 
shaped  ray,  tapering  away  at  both  ends  to  points. 

Planetary  Nebulcs  constitute  another  variety,  and  are 
very  remarkable  objects.  They  have,  as  their  name 
imports,  exactly  the  appearance  of  planets.  Whatever 
may  be  their  nature,  they  must  be  of  enormous  magni- 
tude. One  of  them  is  to  be  found  in  the  parallel  of 
Gamma  Aquarii,  and  about  5m.  preceding  that  star.  Its 
apparent  diameter  is  about  20X/.  Another  in  the  Con- 
stellation Andromeda,  presents  a  visible  disk  of  12",  per- 
fectly defined  and  round.  Granting  these  objects  to  be 


308.  Whatsis  said  of  the  nebula  in  the  sword  of  Orion  ? 
Can  the  nebulae  be  fully  learned  from  description  ? 

309.  Nebulous  stars-r-what  are  they?     What  forms  have 
their  atmospheres  ?    -Planetary  nebulas, — their  appearance  ? 
What  apparent  diameters  have  they  1     What  is  said  of  their 
light  ? 


VARIABLE    STARS.  251 

equally  distant  from  us  with  the  stars,  their  real  dimen- 
sions must  be  such  as,  on  the  lowest  computation,  would 
fill  the  orbit  of  Uranus.  It  is  no  less  evident  that,  if  they 
be  solid  bodies,  of  a  solar  nature,  the  intrinsic  splendor 
of  their  surfaces  must  be  almost  infinitely  inferior  to 
that  of  the  sun.  A  circular  portion  of  the  sun's  disk, 
subtending  an  angle  of  20",  would  give  a  light  equal  to 
100  full  moons  ;  while  the  objects  in  question  are  hardly, 
if  at  all,  discernible  with  the  naked  eye. 

310.  The  Galaxy  or  Milky  Way  is  itself  supposed 
by  some  to  be  a  nebula  of  which  the  sun  forms  a  com- 
ponent part ;  and  hence  it  appears  so  much  greater  than 
other  nebulae  only  in  consequence  of  our  situation  with 
respect  to  it,  and  its  greater  proximity  to  our  system. 
So  crowded  are  the  stars  in  some  parts  of  this  zone,  that 
Sir  William  Herschel,  by  counting  the  stars  in  a  single 
field  of  his  telescope,  estimated  that  50,000  had  passed 
under  his  review  in  a  zone  two  degrees  in  breadth  du- 
ring a  single  hour's  observation.     Notwithstanding  the 
apparent  contiguity  of  the  stars  which  crowd  the  galaxy, 
it  is  certain  that  their  mutual  distances  must  be  incon- 
ceivably great. 

311.  VARIABLE  STARS  are  those  which  undergo  a  pe- 
riodical change  of  brightness.     One  of  the  most  remark- 
able is  the  star  Mira  in  the  Whale,  (Omicron  Ceti.)     It 
appears  once  in  1 1  months,  remains  at  its  greatest  bright- 
ness about  a  fortnight,  being  then,  on  some  occasions, 
equal  to  a  star  of  the  second  magnitude.     It  then  de- 
creases about  three  months,  until  it  becomes  completely 
invisible,  and  remains  so  about  five  months,  when  it 
again  becomes  visible,  and  continues  increasing  during 
the  remaining  three  months  of  its  period. 

Another  very  remarkable  variable  star  is  Algol  (Beta 
Persei.)    It  is  usually  visible  as  a  star  of  the  second  magni- 


310.  Galaxy  or  Milky  Way — what  is  said  respecting  it? 
Give  an  example  of -the  multitude  of  stars  in  it  ? 


252  FIXED    STAKS. 

tude,  and  continues  such  for  2d.  14h.  when  it  suddenly 
begins  to  diminish  in  splendor,  and  in  about  3^  hours  is 
reduced  to  the  fourth  magnitude.  It  then  begins  again 
to  increase,  and  in  3^  hours  more,  is  restored  to  its  usual 
brightness,  going  through  all  its  changes  in  less  than 
three  days.  This  remarkable  law  of  variation  appears 
strongly  to  suggest  the  revolution  round  it  of  some  opake 
body,  which,  when  interposed  between  us  and  Algol, 
cuts  off  a  large  portion  of  its  light.  It  is  (says  Sir  J. 
Herschel)  an  indication  of  a  high  degree  of  activity  in 
regions  where,  but  for  such  evidences,  we  might  con- 
clude all  lifeless.  Our  sun  requires  almost  nine  times 
this  period  to  perform  a  revolution  on  its  axis.  On  the 
other  hand,  the  periodic  time  of  an  opake  revolving 
body,  sufficiently  large,  which  would  produce  a  similar 
temporary  obscuration  of  the  sun,  seen  from  a  fixed  star, 
would  be  less  than  fourteen  hours. 

The  duration  of  these  periods  is  extremely  various. 
While  that  of  Beta  Persei  above  mentioned,  is  less  than 
three  days,  others  are  more  than  a  year,  and  others  many 
years. 

312.  TEMPORARY  STARS  are  new  stars  which  have  ap- 
peared suddenly  in  the  firmament,  and  after  a  certain  in- 
terval, as  suddenly  disappeared  and  returned  no  more. 

It  was  the  appearance  of  a  new  star  of  this  kind  125 
years  before  the  Christian  era,  that  prompted  Hipparchus 
to  draw  up  a  catalogue  of  the  stars,  the  first  on  record. 
Such  also  was  the  star  which  suddenly  shone  out  A.  D 
389,  in  the  Eagle,  as  bright  as  Venus,  and  after  remain- 
ing three  weeks  disappeared  entirely.  At  other  periods, 
at  distant  intervals,  similar  phenomena  have  presented 
themselves.  Thus  the  appearance  of  a  star  in  1572, 
was  so  sudden,  that  Tycho  Brahe  returning  home  one 


311.  Variable  stars — what  are  they  ?    What  is  said  of  Mira  ? 
Also  of  Algol  ?     How  are  their  periods  of  revolution  ? 

312.  Temporary  stars — what  are  they7     Give  examples. 
Do  they  ever  return  ?     Do  stars  ever  disappear  ? 


DOUBLE    STARS.  203 

day  was  surprized  to  find  a  collection  of  country  people 
gazing  at  a  star  which  he  was  sure  did  not  exist  half  an 
hour  before.  It  was  then  as  bright  as  Sirius,  and  con- 
tinued to  increase  until  it  surpassed  Jupiter  when  bright- 
est, and  was  visible  at  mid-day.  In  a  month  it  began 
to  diminish,  and  in  three  months  afterwards  it  had  en- 
tirely disappeared. 

It  has  been  supposed  by  some  that  in  a  few  instances, 
the  same  star  has  returned,  constituting  one  of  the  peri- 
odical or  variable  stars  of  a  long  period. 

Moreover,  on  a  careful  re-examination  of  the  heavens, 
and  a  comparison  of  catalogues,  many  stars  are  now 
found  to  be  missing. 

313.  DOUBLE  STARS  are  those  which  appear  single  to 
the  naked  eye,  but  are  resolved  into  two  by  the  tele- 
scope ;  or,  if  not  visible  to  the  naked  eye,  are  seen  in  the 
telescope  so  close  together  as  to  be  recognized  as  objects 
of  this  class.  Sometimes  three  or  more  stars  are  found 
in  this  near  connexion,  constituting  triple  or  multiple 
stars.  Castor,  for  example,  when  seen  by  the  naked 
eye,  appears  as  a  single  star,  but  in  a  telescope  even  of 
moderate  powers,  it  is  resolved  into  two  stars  of  between 
the  third  and  fourth  magnitudes,  within  5"  of  each  other. 
These  two  stars  are  nearly  of  equal  size,  but  frequently 
one  is  exceedingly  small  in  comparison  with  the  other, 
resembling  a  satellite  near  its  primary,  although  in  dis- 
tance, in  light,  and  in  other  characteristics,  each  has  all 
the  attributes  of  a  star,  and  the  combination  therefore 
cannot  be  that  of  a  planet  with  a  satellite.  In  some  in- 
stances, also,  the  distance  between  these  objects  is  much 
less  than  5",  and  in  many  cases  it  is  less  than  \".  The 
extreme  closeness,  together  with  the  exceeding  minute- 
ness of  most  of  the  double  stars,  requires  the  best  tele- 


313  Double  stars — what  are  they?  What  are  multiple 
stars  ?  Give  an,  example  of  a  double  star  ?  How  do  the  two 
stars  sometimes  differ  ?  What  is  required  in  order  to  observe 
most  of  the  double  stars  ? 

22 


254  FIXED    STARS. 

scopes  united  with  the  most  acute  powers  of  observa- 
tion. Indeed,  certain  of  these  objects  are  regarded  as 
the  severest  tests,  both  of  the  excellence  of  the  instru- 
ment and  of  the  skill  of  the  observer.  The  following 
diagram  represents  four  double  stars,  as  seen  with  ap- 
propriate magnifiers.  No.  1.  exhibits  Epsilon  Bootis  with 
a  power  of  350  ;  No.  2,  Rigel  with  a  power  of  130  ; 
No.  3,  the  Pole-star  with  a  power  of  100  ;  and  No.  4, 
Castor  with  a  power  of  300. 

Fig.  52. 
1  2  3  4 


314.  Our  knowledge  of  the  double  stars  almost  com- 
menced with  Sir  William  Herschel,  about  the  year  1780. 
At  the  time  he  began  his  search  for  them,  he  was  ac- 
quainted with  only  four.  Within  five  years,  he  discov- 
ered nearly  700  double  stars.*  In  his  memoirs,  pub- 
lished in  the  Philosophical  Transactions,  he  gave  most 
accurate  measurements  of  the  distances  between  the  two 
stars,  and  of  the  angle  which  a  line  joining  the  two, 
formed  with  the  parallel  of  declination.  These  data 
would  enable  him,  or  at  least  posterity,  to  judge  whether 
these  minute  bodies  ever  change  their  position  with  re- 
spect to  each  other. 


314.  Who  began  the  discovery  of  double  stars  ?  When  did 
he  publish  his  account  of  them  ?  By  whom  have  these  re- 
searches been  since  prosecuted  1  What  two  circumstances  add 
a  high  degree  of  interest  to  the  phenomena  of  the  double  stars  ? 


During  his  life  he  observed  in  all,  2400  double  stars. 


MOTIONS    OP   THE    FIXED    STARS.  255 

Since  1821,  these  researches  have  been  prosecuted 
with  great  zeal  and  industry  by  Sir  James  South  and 
Sir  John  Herschel  in  England,  and  by  Professor  Struve 
at  Dorpat  in  Russia ;  and  the  whole  number  of  double 
stars  now  known,  amounts  to  several  thousands.  Two 
circumstances  add  a  high  degree  of  interest  to  the  phe- 
nomena of  the  double  stars — the  first  is,  that  a  few  of 
them  at  least  are  found  to  have  a  revolution  around 
each  other,  and  the  second,  that  they  are  supposed  to 
afford  the  means  of  obtaining  the  parallax  of  the  fixed 
stars.  Of  these  topics  we  shall  treat  in  the  next  chapter. 


CHAPTER   III. 

OF   THE    MOTIONS    OF    THE    FIXED    STARS DISTANCES 

NATURE. 

315.  IN  1803,  Sir  William  Herschel  first  determined 
and  announced  to  the  world,  that  there  exist  among  the 
stars,  separate  systems,  composed  of  two  stars  revolving 
about  each  other  in  regular  orbits.  These  he  denomin- 
ated Binary  Stars,  to  distinguish  them  from  other 
double  stars  where  no  such  motion  is  detected,  and 
whose  proximity  to  each  other  may  possibly  arise  from 
casual  juxta-position,  or  from  one  being  in  the  range  of 
the  other.  Between  fifty  and  sixty  instances  of  changes 
to  a  greater  or  less  amount  of  the  relative  position  of 
double  stars,  are  mentioned  by  Sir  William  Herschel ; 
and  a  few  of  them  had  changed  their  places  so  much 
within  25  years,  and  in  such  order,  as  to  lead  him  to  the 
conclusion  that  they  performed  revolutions,  one  around 
the  other,  in  regular  orbits. 


315.  Binary^Stars. — Who  first  discovered  this  class  of 
bodies  ?  How  are  they  distinguished  from  ordinary  double 
stars  1  What  conclusions  did  Sir  W.  Herschel  draw  respect- 
ing them  ? 


'256 


FIXED    STARS. 


316.  These  conclusions  have  been  fully  confirmed  by 
later  observers,  so  that  it  is  now  considered  as  fully  es- 
tablished, that  there  exist  among  the  fixed  stars,  binary 
systems,  in  which  two  stars  perform  to  each  other  the 
office  of  sun  and  planet,  and  that  the  periods  of  revolu- 
tion of  more  than  one  such  pair  have  been  ascertained 
with  something  approaching  to  exactness.  Immersions 
and  emersions  of  stars  behind  each  other  have  been  ob- 
served, and  real  motions  among  them  detected  rapid 
enough  to  become  sensible  and  measurable  in  very  short 
intervals  of  time.  The  following  table  exhibits  the 
present  state  of  our  knowledge  on  this  subject.* 


Names. 

Period  in  years. 

Major  axis  of  the  orbit. 

Eccentricity. 

>?Corona3, 
£Cancri, 
£Ursse  Majoris, 
70  Ophiuchi 
Castor, 
ffCoronae, 
61  Cygni, 
yVirginis, 
vLeonis. 

43.40 
55.00 
58.26 
80.34 
252.66 
286.00 
452.00 
628.90 
1200.00 

7X/.714 
8.784 
16.172 
7.358 
30.860 
24.000 

0.4164 
0.4667 

0.7582 
0.6112 

0.8335 

From  this  table  it  appears,  first,  that  the  periods  of  the 
double  stars  are  very  various,  ranging,  in  the  case  of 
those  already  ascertained,  from  forty-three  years  to  one 


316.  Have  the  conclusions  of  Herschel  been  confirmed  by 
others  ?  What  doctrine  is  now  considered  as  fully  established  ? 
How  are  the  periods  of  the  double  stars  ?  What  is  the  figure  of 
their  orbits  ?  Which  is  the  most  remarkable  of  the  Binary 
stars  ?  What  is  its  size  ?  How  long  since  it  was  first  observed 
to  be  double  ?  What  changes  has  it  undergone  since  ?  When 
did  it  pass  its  perihelion  ? 


*  Those  who  do  not  understand  the  Greek  letters,  can  pass  over  thi» 
table  to  the  inferences  which  follow. 


MOTIONS    OP   THE    FIXED   STARS.  257 

thousand ;  secondly,  that  their  orbits  are  very  small 
ellipses,  more  eccentric  than  those  of  the  planets,  the 
greatest  of  which  (that  of  Mercury)  having  an  eccentri- 
city of  only  about  .2  of  the  major  axis. 

The  most  remarkable  of  the  binary  stars  is  Gamma 
Virginis,  on  account  not  only  of  the  length  of  its  period, 
but  also  of  the  great  diminution  of  apparent  distance, 
and  rapid  increase  of  angular  motion  about  each  other 
of  the  individuals  composing  it.  It  is  a  bright  star  of 
the  fourth  magnitude,  and  its  component  stars  are  almost 
exactly  equal.  It  has  been  known  to  consist  of  two 
stars  since  the  beginning  of  the  eighteenth  century,  their 
distance  being  then  between  six  and  seven  seconds ;  so 
that  any  tolerably  good  telescope  would  resolve  it. 
Since  that  time  they  have  been  constantly  approaching, 
and  are  at  present  hardly  more  than  a  single  second  asun- 
der ;  so  that  no  telescope  that  is  not  of  a  very  superior 
quality,  is  competent  to  show  them  otherwise  than  as  a 
single  star,  somewhat  lengthened  in  one  direction.  It 
fortunately  happens  that  Bradley  (Astronomer  Royal)  in 
1718,  noticed,  and  recorded  in  the  margin  of  one  of  his 
observation  books,  the  apparent  direction  of  their  line  of 
junction,  as  being  parallel  to  that  of  two  remarkable 
stars  Alpha  and  Delta  of  the  same  constellation,  as  seen 
by  the  naked  eye, — a  remark  which  has  been  of  signal 
service  in  the  investigation  of  their  orbit.  It  is  found 
that  it  passed  its  perihelion,  August  18th,  1834. 

317.  The  revolutions  of  the  binary  stars  have  assured 
us  of  that  most  interesting  fact,  that  the  law  of  gravita- 
tion extends  to  the  fixed  stars.  Before  these  discoveries, 
we  could  not  decide  except  by  a  feeble  analogy  that  this 
law  transcended  the  bounds  of  the  solar  system.  In- 


17.  What  great  fact  have  the  revolutions  of  the  binary  stars 
revealed  to  us  ?  How  was  this  doctrine  limited  before  this 
discovery  ?  Are  these  revolutions  those  of  a  planetary  or 
cometary  nature  ? 

22* 


258  FIXED    STARS. 

deed,  our  belief  of  the  fact  rested  more  upon  our  idea  of 
unity  of  design  in  all  the  works  of  the  Creator,  than 
upon  any  certain  proof ;  but  the  revolution  of  one  star 
around  another  in  obedience  to  forces  which  must  be 
similar  to  those  that  govern  the  solar  system,  establishes 
the  grand  conclusion,  that  the  law  of  gravitation  is  truly 
the  law  of  the  material  universe. 

We  have  the  same  evidence  (says  Sir  John  Herschel) 
of  the  revolutions  of  the  binary  stars  about  each  other, 
that  we  have  of  those  of  Saturn  and  Uranus  about  the 
sun ;  and  the  correspondence  between  their  calculated 
and  observed  places  in  such  elongated  ellipses,  must  be 
admitted  to  carry  with  it  a  proof  of  the  prevalence  of  the 
Newtonian  law  of  gravity  in  their  systems,  of  the  very 
same  nature  and  cogency  as  that  of  the  calculated  and 
observed  places  of  comets  round  the  center  of  our  own 
system. 

But  (he  adds)  it  is  not  with  the  revolution  of  bodies 
of  a  planetary  or  cometary  nature  round  a  solar  center 
that  we  are  now  concerned ;  it  is  with  that  of  sun 
around  sun,  each,  perhaps,  accompanied  with  its  train  of 
planets  and  their  satellites,  closely  shrouded  from  our 
view  by  the  splendor  of  their  respective  suns,  and  crowd- 
ed into  a  space,  bearing  hardly  a  greater  proportion  to 
the  enormous  interval  which  separates  them,  than  the 
distances  of  the  satellites  of  our  planets  from  their  pri- 
maries, bear  to  their  distances  from  the  sun  itself. 

318.  Some  of  the  fixed  stars  appear  to  have  a  real  mo- 
tion in  space. 

There  are  several  apparent  changes  of  place  among 
the  stars  which  arise  from  real  changes  in  the  earth, 
which,  as  we  are  not  conscious  of  them,  we  refer  to  the 
stars ;  but  there  are  other  motions  among  the  stars  which 


318.  Have  any  of  the  fixed  stars  a  real  motion  in  space  ? 
Are  the  places  of  the  stars  as  described  in  ancient  times  by 
Ptolemy  nearly  the  same  as  at  present  ?  To  what  conclu- 
sions on  this  subject  are  we  now  forced  ? 


MOTIONS    OP   THE    FIXED    STARS.  259 

cannot  result  from  any  changes  in  the  earth,  but  must 
arise  from  changes  in  the  stars  themselves.  Such  mo- 
tions are  called  the  proper  motions  of  the  stars.  Nearly 
2000  years  ago,  Hipparchus  and  Ptolemy  made  the  most 
accurate  determinations  in  their  power  of  the  relative 
situations  of  the  stars,  and  their  observations  have  been 
transmitted  to  us  in  Ptolemy's  Almagest ;  from  which  it 
appears  that  the  stars  retain  at  least  very  nearly  the  same 
places  now  as  they  did  at  that  period.  Still  the  more 
accurate  methods  of  modern  Astronomers,  have  brought 
to  light  minute  changes  in  the  places  of  certain  stars, 
which  force  upon  us  the  conclusion,  either  that  our  solar 
system  causes  an  apparent  displacement  of  certain  stars, 
by  a  motion  of  its  own  in  space,  or  that  they  have  them- 
selves a  proper  motion.  Possibly,  indeed,  both  these 
causes  may  operate. 

319.  If  the  sun,  and  of  course  the  earth  which  accom- 
panies him,  is  actually  in  motion,  the  fact  may  become 
manifest  from  the  apparent  approach  of  the  stars  in  the 
region  which  he  is  leaving,  and  the  recession  of  those 
which  lie  in  the  part  of  the  heavens  towards  which  he 
is  travelling.  Were  two  groves  of  trees  situated  on  a 
plain  at  some  distance  apart,  and  we  should  go  from  one 
to  the  other,  the  trees  before  us  would  gradually  appear 
farther  and  farther  asunder,  while  those  we  left  behind 
would  appear  to  approach  each  other.  Some  years  since, 
Sir  William  Herschel  supposed  he  had  detected  changes 
of  this  kind  among  two  sets  of  stars  in  opposite  points 
of  the  heavens,  and  announced  that  the  solar  system 
was  in  motion  towards  a  point  in  the  constellation  Her- 
cules ;  but  other  astronomers  have  not  found  the  changes 
«  question  such  as  would  correspond  to  this  motion,  or 


319.  If  the  solar  system  is  really  in  motion,  how  may  the 
fact  become  manifest  ?  Towards  what  constellation  did  Sir 
William  Herschel  suppose  it  moving  ?  Has  the  opinion  been 
confirmed  by  later  observers  ? 


260  FIXED    STARS. 

to  any  motion  of  the  sun ;  and  while  it  is  a  matter  of 
general  belief  that  the  sun  has  a  motion  in  space,  the 
fact  is  not  considered  as  yet  entirely  proved 

320.  In  most  cases  where  a  proper  motion  in  certain 
stars  has  been  suspected,  its  annual  amount  has  been  so 
small,  that  many  years  are  required  to  assure  us,  that  the 
effect  is  not  owing  to  some  other  cause  than  a  real  pro- 
gressive motion  in  the  stars  themselves-;  but  in  a  few 
instances  the  fact  is  too  obvious  to  admit  of  any  doubt. 
Thus  the  two  stars  61  Cygni,  which  are  nearly  equal, 
have  remained  constantly  at  the  same,  or  nearly  at  the 
same  distance  of  15"  for  at  least  fifty  years  past.     Mean- 
while  they  have   shifted   their   local   situation   in  the 
heavens,  4?  23"  the  annual  proper  motion  of  each  star 
being  5/x.3,  by  which  quantity  this  system  is  every  year 
carried  along  in  some  unknown  path,  by  a  motion  which 
for  many  centuries  must  be  regarded  as  uniform  and  rec- 
tillinear.     A  greater  proportion  of  the  double  stars  than 
of  any  other  indicate  proper  motions,  especially  the  bi- 
nary stars  or  those  which  have  a  revolution  around  each 
other.     Among  stars  not  double,  and  no  way  differing 
from  the  rest  in  any  other  obvious  particular,  Mu  Cassi- 
opeia has  the  greatest  proper  motion  of  any  yet  ascer- 
tained, amounting  to  nearly  4"  annually. 

DISTANCES    OF   THE    FIXED   STARS. 

321.  We  cannot  ascertain  the  actual  distance  of  any 
of  the  fixed  stars,  but  can  certainly  determine  that  the 
nearest  star  is  more  than  (20,000,000,000,000,)  twenty 
billions  of  miles  from  the  earth. 


320.  What  length  of  time  is  required  in  order  to  detect 
proper  motions  in  the  stars  ?  What  changes  have  occurred  in 
the  two  stars  61  Cygni?  What  sort  of  stars  indicate  proper 
motions  ?  Of  stars  not  double,  what  star  has  the  greatest 
proper  motion  ? 


DISTANCES    OF   THE    FIXED    STARS.  261 

For  all  the  measurements  relating  to  the  distances  of 
the  sun  and  planets,  the  radius  of  the  earth  furnishes  the 
base  line.  (Art.  96.)  The  length  of  this  line  being 
known,  and  the  horizontal  parallax  of  the  body,  whose 
distance  is  sought,  we  readily  obtain  the  distance  by  tne 
solution  of  a  right  angled  triangle.  But  any  star  viewed 
from  the  opposite  sides  of  the  earth,  would  appear  from 
Doth  stations,  to  occupy  precisely  the  same  situation  in 
the  celestial  sphere,  and  of  course  it  would  exhibit  no 
horizontal  parallax. 

But  astronomers  have  endeavored  to  find  a  parallax  in 
some  of  the  fixed  stars,  by  taking  the  diameter  of  the 
earths  orbit  as  a  base  line.  Yet  even  a  change  of  posi- 
tion amounting  to  190  millions  of  miles,  proves  insuffi- 
cient to  alter  the  place  of  a  single  star,  from  which  it  is 
concluded  that  the  stars  have  not  even  any  annual  par- 
allax ;  that  is,  the  angle  subtended  by  the  semi-diameter 
of  the  earth's  orbit,  at  the  nearest  fixed  star  is  insensible. 
The  errors  to  which  instrumental  measurements  are  sub- 
ject, arising  from  the  defects  of  the  instruments  them- 
selves, from  refraction,  and  from  various  other  sources  of 
inaccuracy,  are  such,  that  the  angular  determinations  of 
arcs  of  the  heavens  cannot  be  relied  on  to  less  than  I". 
But  the  change  of  place  in  any  star  when  viewed  at  op- 
posite extremities  of  the  earth's  orbit,  is  less  than  1",  and 
therefore  cannot  be  appreciated  by  direct  measurement. 
It  follows,  that,  when  viewed  from  the  nearest  star,  the 
diameter  of  the  earth's  orbit  would  be  insensible. 

322.  Taking,  however,  the  annual  parallax  of  a  fixed 
star  at  1",  it  can  be  demonstrated  that  the  distance  of 
the  nearest  fixed  star  must  exceed  95000000x200000— 
190000000x100000,  or  one  hundred  thousand  times 


321 .  What  do  we  know  respecting  the  distances  of  the  fixed 
stars  ?  Have  the  fixed  stars  any  parallax  ?  What  is  taken  as 
the  base  line  for  measuring  the  parallax  ?  What  angle  is 
greater  than  would  be  subtended  by  the  diameter  of  the  earth's 
oirbit  as  seen  from  the  nearest  fixed  star  ? 


262  FIXED    STABS. 

one  hundred  and  ninety  millions  of  miles.  Of  a  dis- 
tance so  vast  we  can  form  no  adequate  conceptions,  and 
even  seek  to  measure  it  only  by  the  time  that  light, 
(which  moves  more  than  192,000  miles  per  second,  and 
passes  from  the  sun  to  the  earth  in  8m.  13.3sec.,)  would 
take  to  traverse  it,  which  is  found  to  be  more  than  threv 
and  a  half  years. 

If  these  conclusions  are  drawn  with  respect  to  the 
largest  of  the  fixed  stars,  which  we  suppose  to  be  vastly 
nearer  to  us  than  those  of  the  smallest  magnitude,  the 
idea  of  distance  swells  upon  us  when  we  attempt  to  es- 
timate the  remoteness  of  the  latter.  As  it  is  uncertain, 
however,  whether  the  difference  in  the  apparent  magni- 
tudes of  the  stars  is  owing  to  a  real  difference,  or  merely 
to  their  being  at  various  distances  from  the  eye,  more  or 
less  uncertainty  must  attend  all  efforts  to  determine  the 
relative  distances  of  the  stars ;  but  astronomers  generally 
believe,  that  the  lower  orders  of  stars  are  vastly  more 
distant  from  us  than  the  higher.  Of  some  stars  it  is 
said,  that  thousands  of  years  would  be  required  for  their 
light  to  travel  down  to  us. 

323.  We  have  said  that  the  stars  have  no  annual  par- 
allax ;  yet  it  may  be  observed  that  astronomers  are  not 
exactly  agreed  on  this  point.  Dr.  Brinkley,  a  late  emi- 
nent Irish  astronomer,  supposed  that  he  had  detected  an 
annual  parallax  in  Alpha  Lyrae  amounting  to  lx/.13  and 
in  Alpha  Aquilae  of  lx/.42.  These  results  were  contro- 
verted by  Mr.  Pond,  of  the  Royal  Observatory  of  Green- 
wich ;  and  Mr.  Struve  of  Dorpat,  has  shown  that  in  a 
number  of  cases,  the  parallax  is  in  a  direction  opposite 
to  that  which  would  arise  from  the  motion  of  the  earth. 
Hence  it  is  considered  doubtful  whether  in  all  cases  of 


322.  If  we  take  the  parallax  at  1",  what  must  the  distance 
be  ?     What  time  would  it  take  light  to  traverse  this  space  1 
How  much  farther  off  than  this  may  some  of  the  smaller  stars  be? 

323.  Is  it  entirely  settled  that  the  fixed  stars  have  no  paral- 
lax ?     What  did  Dr.  Brinkley  assert  1     Have  his  observations 
been  confirmed  ? 


DISTANCE    OF    THE    FIXED  STARS.  263 

an  apparent  parallax,  the  effect  is  not  wholly  due  to 
errors  of  observation. 

324.  Indirect  methods  have  been  proposed  for  ascer- 
taining the  parallax  of  the  fixed  stars  by  means  of  obser- 
vations on  the  double  stars.  If  the  two  stars  composing 
a  double  star  are  at  different  distances  from  us,  parallax 
would  affect  them  unequally,  and  change  their  relative 
positions  with  respect  to  each  other ;  and  since  the  ordi- 
nary sources  of  error  arising  from  the  imperfection  of 
instruments,  from  precession,  and  refraction,  would  be 
avoided,  (since  they  would  affect  both  objects  alike,  and 
therefore  would  not  disturb  their  relative  positions,) 
measurements  taken  with  the  micrometer  of  changes 
much  less  than  \"  may  be  relied  on.  Sir  John  Herschel 
proposes  a  method  by  which  changes  may  be  determined 
which  amount  to  only  ^  of  a  second.* 

The  immense  distance  of  the  fixed  stars  is  inferred 
also  from  the  fact,  that  the  largest  telescopes  do  not  in- 
crease their  apparent  magnitude.  They  are  still  points, 
when  viewed  with  the  highest  magnifiers,  although 
they  sometimes  present  a  spurious  disk,  which  is  owing 
to  irradiation.'f 


324.  What  indirect  methods  have  been  proposed  for  ascer- 
taining the  parallax  of  the  fixed  stars  ?  State  the  particulars 
of  this  method.  How  minute  changes  of  place  is  it  supposed 
may  be  detected.  How  do  the  largest  telescopes  affect  their 
apparent  magnitudes  ? 


*  Very  recent  intelligence  informs  us,  that  Prof.  Bessel  of  Konigs- 
berg,  has  obtained  decisive  evidence  of  an  annual  parallax  in  61  Cygni, 
amounting  to  0"  .3136.  This  makes  the  distance  of  that  star,  equal  to 
657700  times  95  millions  of  miles — a  distance  which  it  would  take  light 
10.3  years  to  traverse. 

t  Irradiation  is  an  enlargement  of  objects  beyond  their  proper  bounds, 
in  consequence  of  the  vivid  impression  of  light  on  the  eye.  It  is  sup- 
posed to  increase  the  apparent  diameters  of  the  sun  and  moon  from  three 
to  four  seconds,  and  to  create  an  appearance  of  a  disk  in  a  fixed  star, 
which,  when  this  cause  is  removed,  ia  seen  as  a  mere  point. 


264  FIXED    STARS. 


NATURE    OF   THE    STARS. 

325.  The  stars  are  bodies  greater  than  our  earth.     If 
this  were  not  the  case  they  could  not  be  visible  at  such 
an  immense  distance.     Dr.  Wollaston,  a  distinguished 
English  philosopher,  attempted  to  estimate  the  magni- 
tudes of  certain  of  the  fixed  stars  from  the  light  which 
they  afford.     By  means  of  an  accurate  photometer  (an 
instrument  for  measuring  the  relative  intensities  of  light) 
he  compared  the  light  of  Sirius  with  that  of  the  sun. 
He  next  inquired  how  far  the  sun  must  be  removed  from 
us  in  order  to  appear  no  brighter  than  Sirius.     He  found 
the  distance  to  be  141,400  times  its  present  distance. 
But  Sirius  is  more  than  200,000  times  as  far  off  as  the 
sun.     Hence  he  inferred  that,  upon  the  lowest  compu- 
tation, Sirius  must  actually  give  out  twice  as  much 
light  as  the  sun ;  or  that,  in  point  of  splendor,  Sirius 
must  be  at  least  equal  to  two  suns.     Indeed,  he  has  ren- 
dered it  probable  that  the  light  of  Sirius  is  equal  to 
fourteen  suns. 

326.  The  fixed  stars  are  suns.     We  have  already  seen 
that   they  are  large  bodies ;   that  they  are  immensely 
farther  off  than  the  farthest  planet ;  that  they  shine  by 
their  own  light ;  in  short,  that  their  appearance  is,  in  all 
respects,  the  same  as  the  sun  would  exhibit  if  removed 
to  the  region  of  the  stars.     Hence  we  infer,  that  they 
are  bodies  of  the  same  kind  with  the  sun. 

We  are  justified  therefore  by  a  sound  analogy,  in  con- 
cluding that  the  stars  were  made  for  the  same  end  as 
the  sun,  namely,  as  the  centers  of  attraction  to  other 
planetary  worlds,  to  which  they  severally  dispense  light 
and  heat.  Although  the  starry  heavens  present,  in  a 
clear  night,  a  spectacle  of  ineffable  grandeur  and  beauty, 


325.  Nature  of  the  stars.  How  large  are  the  stars  compared 
with  the  earth  ?  How  did  Dr.  Wollaston  endeavor  to  estimate 
the  magnitudes  of  certain  fixed  stars  ?  How  distant  would  this 
method  make  Sirius ?  T  *  how  many  suns  is  Sirius  equal  ? 


SYSTEM    OP   THE    WORLD.  265 

yet  it  must  be  admitted  that  the  chief  purpose  of  the 
stars  could  not  have  been  to  adorn  the  night,  since  by 
far  the  greatest  part  of  them  are  wholly  invisible  to  the 
naked  eye  ;  nor  as  landmarks  to  the  navigator,  for  only  a 
very  small  proportion  of  them  are  adapted  to  this  pur- 
pose ;  nor,  finally,  to  influence  the  earth  by  their  attrac- 
tions, since  their  distance  renders  such  an  effect  entirely 
insensible.  If  they  are  suns,  and  if  they  exert  no  im- 
portant agencies  upon  our  world,  but  are  bodies  evidently 
adapted  to  the  same  purpose  as  our  sun,  then  it  is  as  ra- 
tional to  suppose  that  they  were  made  to  give  light  and 
heat,  as  that  the  eye  was  made  for  seeing  and  the  ear 
for  hearing.  It  is  obvious  to  inquire  next,  to  what  they 
dispense  these  gifts  if  not  to  planetary  worlds ;  and  why 
to  planetary  worlds,  if  not  for  the  use  of  percipient  be- 
ings ?  We  are  thus  led,  almost  inevitably,  to  the  idea 
of  a  Plurality  of  Worlds  ;  and  the  conclusion  is  forced 
upon  us,  that  the  spot  which  the  Creator  has  assigned  to 
us  is  but  a  humble  province  of  his  boundless  empire.* 


CHAPTER  IV. 


OP   THE    SYSTEM   OP   THE  WORLD. 

327.  The  arrangement  of  all  the  bodies  that  compose 
the  material  universe,  and  their  relations  to  each  other, 
constitute  the  System  of  the  World. 

It  is  otherwise  called  the  Mechanism  of  the  Heavens ; 
and  indeed,  in  the  System  of  the  World,  we  figure  to 
ourselves  a  machine,  all  the  parts  of  which  have  a  mu- 


326.  Prove  that  the  fixed  stars  are  suns.  For  what  purpose 
were  they  made  ?  Could  they  have  been  designed  to  adorn  the 
night  ?  or  as  landmarks  to  the  navigator  ?  If  they  are  suns,  for 
what  farther  purpose  were  they  designed  ? 

*  See  this  argument,  in  its  full  extent,  in  Dick's  Celestial  Scer,ery. 
23 


266  SYSTEM    OF    THE    WORLD. 

tual  dependence,  and  conspire  to  one  great  end.  "  The 
machines  that  are  first  invented  (says  Adam  Smith)  to 
perform  any  particular  movement,  are  always  the  most 
complex ;  and  succeeding  artists  generally  discover  that 
with  fewer  wheels  and  with  fewer  principles  of  motion 
than  had  originally  been  employed,  the  same  effects  may 
be  more  easily  produced.  The  first  systems,  in  the 
same  manner,  are  always  the  most  complex  ;  and  a  par- 
ticular connecting  chain  or  principle  is  generally  thought 
necessary  to  unite  every  two  seemingly  disjointed  ap- 
pearances ;  but  it  often  happens,  that  one  great  cpnnect- 
ing  principle  is  afterwards  found  to  be  sufficient,  to  bind 
together  all  the  discordant  phenomena  that  occur  in  a 
whole  species  of  things."  This  remark  is  strikingly 
applicable  to  the  origin  and  progress  of  systems  of  as 
tronomy. 

328.  From  the  visionary  notions  which  are  generally 
understood  to  have  been  entertained  on  this  subject  by 
the  ancients,  we  are  apt  to  imagine  that  they  knew  less 
than  they  actually  did  of  the  truths  of  astronomy.  But 
Pythagoras,  who  lived  500  years  before  the  Christian 
era,  was  acquainted  with  many  important  facts  in  our 
science,  and  entertained  many  opinions  respecting  the 
system  of  the  world  which  are  now  held  to  be  true. 
Among  other  things  well  known  to  Pythagoras  were  the 
following : 

1.  The  principal  Constellations.     These  had  begun  to 
be  formed  in  the  earliest  ages  of  the  world.     Several  of 
them  bearing  the  same  names  as  at  present,  are  men- 
tioned in  the  writings  of  Hesiod  and  Homer ;  and  tile 
*•  sweet  influences  of  the  Pleiades"  and  the  "  bands  of 
Orion,"  are  beautifully  alluded  to  in  the  book  of  Job. 

2.  Eclipses.     Pythagoras  knew  both  the  causes  of 
eclipses  and  how  to  predict  them ;  not  indeed  in  the  ac- 


327.  What  constitutes  the  System  of  the  World  ?  Under 
what  image  do  we  figure  it  to  ourselves  ?  What  properties 
characterize  the  machines  first  invented  ? 


ASTRONOMICAL   KNOWLEDGE    OF   THE    ANCIENTS.        267 

curate  manner  now  employed,  but  by  means  of  the  Saros. 
(Art.  168.) 

3.  Pythagoras  had  divined  the  true  system  of  the 
world,  holding  that  the  sun  and  not  the  earth,  (as  was 
generally  held  by  the  ancients,  even  for  many  ages  after 
Pythagoras,)  is  the  center  around  which  all  the  planets 
revolve,  and  that  the  stars  are  so  many  suns,  each  the 
center  of  a  system  like  our  own.  Among  lesser  things, 
he  knew  that  the  earth  is  round ;  that  its  surface  is  nat- 
urally divided  into  five  Zones ;  and  that  the  ecliptic  is 
inclined  to  the  equator.  He  also  held  that  the  earth  re- 
volves daily  on  its  axis,  and  yearly  around  the  sun ;  that 
the  galaxy  is  an  assemblage  of  small  stars ;  and  that  it 
is  the  same  luminary,  namely,  Venus,  that  constitutes 
bofh  the  morning  and  the  evening  star,  whereas,  all  the 
ancients  before  him  had  supposed  that  each  was  a  sepa- 
rate planet,  and  accordingly  the  morning  star  was  called 
Lucifer,  and  the  evening  star  Hesperus.  He  held  also 
that  the  planets  were  inhabited,  and  even  went  so  far  as 
to  calculate  the  size  of  some  of  the  animals  in  the  moon. 
Pythagoras  was  so  great  an  enthusiast  in  music,  that  he 
not  only  assigned  to  it  a  conspicuous  place  in  his  system 
of  education,  but  even  supposed  the  heavenly  bodies 
themselves  to  be  arranged  at  distances  corresponding  to 
the  diatonic  scale,  and  imagined  them  to  pursue  their  sub- 
lime march  to  notes  created  by  their  own  harmonious 
movements,  called  the  "  music  of  the  spheres  ;"  but  he 
maintained  that  this  celestial  concert,  though  loud  and 
grand,  is  not  audible  to  the  feeble  organs  of  man,  but 
only  to  the  gods. 

329.  With  few  exceptions,  however,  the  opinions  of 
Pythagoras  on  the  System  of  the  World,  were  founded 


328.  What  is  said  of  our  usual  estimate  of  the  knowledge  of 
astronomy  possessed  by  the  ancients  1  What  things  were 
known  to  Pythagoras  ?  How  early  were  the  principal  constel- 
lations known  1  What  did  Pythagoras  know  of  eclipses  ?  Also 
respecting  the  System  of  the  World  ?  What  lesser  things  did 
he  know  ?  What  notions  had  he  of  the  music  of  the  spheres  ? 


'268  SYSTEM    OF   THE    WORLD. 

in  truth.  Yet  they  were  rejected  by  Aristotle  and  by 
most  succeeding  astronomers  down  to  the  time  of  Coper- 
nicus, and  in  their  place  was  substituted  the  doctrine  of 
Crystalline  Spheres,  first  taught  by  Eudoxus.  Accord- 
ing to  this  system,  the  heavenly  bodies  are  set  like  gems 
in  hollow  solid  orbs,  composed  of  crystal  so  pellucid  that 
no  anterior  orb  obstructs  in  the  least  the  view  of  any  of 
the  orbs  that  lie  behind  it.  The  sun  and  the  planets 
have  each  its  separate  orb ;  but  the  fixed  stars  are  all  set 
in  the  same  grand  orb  ;  and  beyond  this  is  another  still, 
the  Primum  Mobile,  which  revolves  daily  from  east  to 
west,  and  carries  along  with  it  all  the  other  orbs.  Above 
the  whole,  spreads  the  Grand  Empyrean,  or  third  heav- 
ens, the  abode  of  perpetual  serenity. 

To  account  for  the  planetary  motions,  it  was  supposed 
that  each  of  the  planetary  orbs  as  well  as  that  of  the  sun, 
has  a  motion  of  its  own  eastward,  while  it  partakes  of 
the  common  diurnal  motion  of  the  starry  sphere.  Aris- 
totle taught  that  these  motions  are  effected  by  a  tutelary 
genius  of  each  planet,  residing  in  it,  and  directing  its 
motions,  as  the  mind  of  man  directs  his  motions. 

330.  On  coming  down  to  the  time  of  Hipparchus,  who 
flourished  about  150  years  before  the  Christian  era,  we 
meet  with  astronomers  who  acquired  far  more  accurate 
knowledge  of  the  celestial  motions.  Previous  to  this 
period,  celestial  observations  were  made  chiefly  with  the 
naked  eye,  but  Hipparchus  was  in  possession  of  instru- 
ments for  measuring  angles,  and  knew  how  to  resolve 
spherical  triangles.  He  ascertained  the  length  of  the 
year  within  6m.  of  the  truth.  He  discovered  the  eccen- 
tricity of  the  solar  orbit,  (although  he  supposed  the  sun 
actually  to  move  uniformly  in  a  circle,  but  the  earth  to 
be  placed  out  of  the  center,)  and  the  positions  of  the 


329.  Were  the  opinions  of  Pythagoras  generally  embraced 
by   the   ancients  ?     What   was   the   doctrine  of  Crystalline 
Spheres  ?     How  were  the  planetary  motions  accounted  for  ? 

330.  When  did  Hipparchus  flourish  ?     How  did  he  make 
his  observations  ?     What  great  facts  did  he  ascertain  ? 


THE    PTOLEMAIC    SYSTEM.  269 

sun's  apogee  and  perigee.  He  formed  very  accurate  es- 
timates of  the  obliquity  of  the  ecliptic,  and  of  the  preces- 
sion of  the  equinoxes.  He  computed  the  exact  period 
of  the  synodic  revolution  of  the  moon,  and  the  inclina- 
tion of  the  lunar  orbit ;  discovered  the  motion  of  her 
node  and  of  her  line  of  apsides  ;  and  made  the  first  at- 
tempts to  ascertain  the  horizontal  parallaxes  of  the  sun 
and  moon. 

Such  was  the  state  of  astronomical  knowledge  when 
Ptolemy  wrote  the  Almagest,  in  which  he  has  transmit- 
ted to  us  an  encyclopedia  of  the  astronomy  of  the  an- 
cients. 

331.  The  systems  of  the  world  which  have  been  most 
celebrated  are  three — the  Ptolemaic,  the  Tychonic,  and 
the  Copernican.     We  shall  conclude  this  part  of  our 
work  with  a  concise  statement  and  discussion  of  each 
of  th&se  systems  of  the  Mechanism  of  the  Heavens. 

THE    PTOLEMAIC    SYSTEM.  * 

332.  The  doctrines  of  the  Ptolemaic  System  were  not 
originated  by  Ptolemy,  but  being  digested  by  him  out  of 
materials  furnished  by  various  hands,  it  has  come  down 
to  us  under  the  sanction  of  his  name. 

According  to  this  system,  the  earth  is  the  center  of 
the  universe,  and  all  the  heavenly  bodies  daily  revolve 
around  it  from  east  to  west.  In  order  to  explain  the 
planetary  motions,  Ptolemy  had  recourse  to  deferents  and 
epicycles — an  explanation  devised  by  Apollonius  one  of 
the  greatest  geometers  of  antiquity.  He  conceived  that, 
in  the  circumference  of  a  circle,  having  the  earth  for  its 
center,  there  moves  the  center  of  another  circle,  in  the 
circumference  of  which  the  planet  actually  revolves. 
The  circle  surrounding  the  earth  was  called  the  deferent. 


331.  What  are  the  most  celebrated  Systems  of  the  World? 

332.  Ptolemaic  System. — Did  Ptolemy  originate  this  sys- 
tem?    State  the   outlines  of  it.     What  was   the  deferent? 
What  was  the  epicycle  ? 

23* 


270 


SYSTEM    OF   THE    WORLD. 


while  the  smaller  circle  whose  center  was  always  in  the 
periphery  of  the  deferent,  was  called  the  epicycle.  The 
motion  in  each  was  supposed  to  be  uniform.  Lastly,  it 
was  conceived  that  the  motion  of  the  center  of  the  epi- 
cycle in  the  circumference  of  the  deferent,  and  of  the 
planet  in  that  of  the  epicycle,  are  in  the  same  directions. 

333.  But  these  views  will  be  better  understood  from  a 
diagram.  Therefore,  let  ABC  (Fig.  53,)  represent  the 
deferent,  E  being  the  earth  a  little  out  of  the  center. 


Let  abc  represent  the  epicycle,  having  its  center  at  v,  on 
the  periphery  of  the  deferent.  Conceive  the  circumfer- 
ence of  the  deferent  to  be  carried  about  the  earth  every 
twenty  four  hours  in  the  order  of  the  letters  ;  and  at  the 


333.  Explain  the  Ptolemaic  System  by  figure  53. 


THE    PTOLEMAIC   SYSTEM.  271 

same  time,  let  the  center  v  of  the  epicycle  abed,  have  a 
slow  motion  in  the  opposite  direction,  and  let  a  body  re- 
volve in  this  circle  in  the  direction  abed.  Then  a  body 
revolving  in  the  circle  abed,  and  at  the  same  time  having 
a  motion  eastward  in  common  with  the  circle,  would 
describe  the  looped  curves  khnnop.  At  I  and  m,  and  at 
n  and  o,  it  would  appear  stationary,  because  in  these 
points  its  motion  would  be  either  directly  towards  or 
from  the  spectator.  The  motion  would  be  direct  from 
k  to  /,  being  in  the  order  of  the  signs,  and  retrograde 
from  I  to  m  ;  direct  again  from  m  to  n,  and  retrograde 
from  n  to  o. 

334.  Such  a  deferent  and  epicycle  may  be  devised 
for  each  planet  as  will  fully  explain  all  its  ordinary  mo- 
tions ;  but  it  is  inconsistent  with  the  phases  of  Mercuiy 
and  Venus,  which  being  between  us  and  the  sun  on 
both  sides  of  the  epicycle,  would  present   their  dark 
sides  towards  us  in  both  these  positions,  whereas  at  one 
of  the  conjunctions   they  are  seen  to  shine  with  full 
face.     It  is  moreover  absurd  to  speak  of  a  geometrical 
center  which  has  no  bodily  existence,  moving  around  the 
earth  on  the  circumference  of  another  circle ;  and  hence 
some  suppose  that  the  ancients  merely  assumed  this  hy- 
pothesis as  affording  a  convenient  geometrical  represen- 
tation of  the  Phenomena, — a  diagram  simply,  without 
conceiving  the  system  to  have  any  real  existence  in  na- 
ture. 

335.  The  objections  to  the  Ptolemaic  system,  in  gen- 
eral, are  the  following :  First,  it  is  a  mere  hypothesis, 
having  no  evidence  in  its  favor,  except  that  it  explains 
the  phenomena.     Tljis  evidence  is  insufficient  of  itself, 
since  it  frequently  happens  that  each  of  two  hypotheses, 


334.  State  the  objections  to  this  mode  of  representing  the 
motions  of  the  planets.  Why  is  it  inconsistent  with  the  phases 
of  Mercury  and  Venus  ?  What  is  said  of  the  supposition  of  a 
geometrical  center  moving  around  the  earth  ? 


'272  SYSTEM    OP   THE    WORLD. 

directly  opposite  to  each  other,  will  explain  all  the  known 
phenomena.  But  the  Ptolemaic  system  does  not  even 
do  this,  as  it  is  inconsistent  with  the  phaaes  of  Mercury 
and  Venus,  as  already  observed.  Secondly,  now  that 
we  are  acquainted  with  the  distances  of  the  remoter 
planets,  and  especially  of  the  fixed  stars,  the  swiftness 
of  motion  implied  in  a  daily  revolution  of  the  starry 
firmament  around  the  earth,  renders  such  a  motion 
wholly  incredible.  Thirdly,  the  centrifugal  force  that 
would  be  generated  in  these  bodies,  especially  in  the 
sun,  renders  it  impossible  that  they  can  continue  to  re- 
volve around  the  earth  as  a  center. 

These  reasons  are  sufficient  to  show  the  absurdities 
of  the  Ptolemaic  System  of  the  World. 

THE    TYCHONIC    SYSTEM. 

336.  Tycho  Brahe,  like  Ptolemy,  placed  the  earth  in 
the  center  of  the  universe,  and  accounted  for  the  diur- 
nal motions  in  the  same  manner  as  Ptolemy  had  done, 
namely,  by  an  actual  revolution  of  the  whole  host  of 
heaven  around  the  earth  every  twenty  four  hours.     But 
he  rejected  the  scheme  of  deferents  and  epicycles,  and 
held  that  the  moon  revolves  about  the  earth  as  the  cen- 
ter of  her  motions ;  that  the  sun  and  not  the  earth,  is 
the  center  of  the  planetary  motions ;  and  that  the  sun 
accompanied   by  the  planets  moves  around  the  earth 
once  a  year,  somewhat  in  the  manner  that  we  now  con- 
ceive of  Jupiter  and  his  satellites  as  revolving  around 
the  sun. 

337.  The  system  of  Tycho  serves  to  explain  all  the 
common  phenomena  of  the  planetary  motions,  but  it  is 
encumbered  with  the  same  objections  as  those  that  have 


335.  State  the  objections  to  the  Ptolemaic  System  in  general. 
Does  it  explain  all  the  phenomena  ?   What  swiftness  of  motion 
does  it  imply  ? 

336.  Tychonic  System. — State  its  leading  points. 


THE    COPERNICAN    SYSTEM.  273 

been  mentioned  as  resting  against  the  Ptolemaic  system, 
namely,  that  it  is  a  mere  hypothesis ;  that  it  implies  an 
incredible  swiftness  in  the  diurnal  motions ;  and  that  it 
is  inconsistent  with  the  known  laws  of  unive/sal  grav- 
itation. But  if  the  heavens  do  not  revolve,  the  earth 
must,  and  this  brings  us  to  the  system  of  Copernicus. 

THE  "COPERNICAN    SYSTEM. 

338.  Copernicus  was  born  at  Thorn  in  Prussia  in 
1473.  The  system  that  bears  his  name  was  the  fruit  of 
forty  years  of  intense  study  and  meditation  upon  the 
celestial  motions.  As  already  mentioned,  (Art.  6,)  it 
maintains  (1)  That  the  apparent  diurnal  motions  of  the 
heavenly  bodies,  from  east  to  west  is  owing  to  the  real 
revolution  of  the  earth  on  its  own  axis  from  west  to  east ; 
and  (2)  That  the  sun  is  the  center  around  which  the 
earth  and  planets  all  revolve  from  west  to  east.  It  rests 
on  the  following  arguments : 

First,  the  earth  revolves  on  its  own  axis. 

1.  Because  this  supposition  is  vastly  more  simple. 

2.  It  is  agreeable  to  analogy,  since  all  the  other  plan- 
ets that  afford  any  means  of  determining  the  question, 
are  seen  to  revolve  on  their  axes. 

3.  The  spheriodal  figure  of  the  earth,  is  the  figure  of 
equilibrium,  that  results  from  a  revolution  on  its  axis. 

4.  The  diminished  weight  of  bodies  at  the  equator, 
indicates  a  centrifugal  force  arising  from  such  a  rev- 
olution. 

5.  Bodies  let  fall  from  a  high  eminence,  fall  eastward 
of  their  base,  indicating  that  when  farther  from  the  cen- 
ter of  the  earth  they  were  subject  to  a  greater  velocity, 
which  in  consequence  of  their  inertia,  they  do  not  en- 
tirely lose  in  descending  to  the  lower  level. 


337.  How  far  does  the  Tychonic  System  explain  the  plan- 
etary motions  ?     With  what  objections  is  it  encumbered  ? 

338.  Copernican  System. — Who  was  Copernicus  ?     State' 
the  principles  of  his  System.     State  the  five  reasons  why  tho 
earth  revolves  on  its  axis. 


#74  SYSTEM    OP   THE    WORLD. 

339.  Secondly,  the  planets,  including  the  earth,  revolve 
about  the  sun. 

1.  The  phases  of  Mercury  and  Venus  are  precisely 
such,  as  would  result  from  their  circulating  around  the 
sun  in  orbits  within  that  of  the  earth ;   but  they  are 
never  seen  in  opposition,  as  they  would  be  if  they  cir- 
culate around  the  earth. 

2.  The  superior  planets  do  indeed  revolve  around  the 
earth ;  but  they  also  revolve  around  the  sun,  as  is  evi- 
dent from  their  phases  and  from  the  known  dimensions 
of  their  orbits ;  and  that  the  sun  and  not  the  earth,  is  the 
center  of  their  motions,  is  inferred  from  the  greater  sym- 
metry of  their  motions  as  referred  to  the  sun  than  as  re- 
ferred to  the  earth,  and  especially  from  the  laws  of  grav- 
itation which  forbid  our  supposing  that  bodies  so  much 
larger  than  the  earth,  as  some  of  these  bodies  are,  can 
circulate  permanently  around  the  earth,  the  latter  re- 
maining all  the  while  at  rest. 

3.  The  annual  motion  of  the  earth  itself  is  indicated 
also  by  the  most  conclusive  arguments.     For,  first,  since 
all  the  planets  with  their  satellites,  and  the  comets,  re- 
volve about  the  sun,  analogy  leads  us  to  infer  the  same 
respecting  the  earth  and  its  satellites.     Secondly,  The 
motions  of  the  satellites,  as  those  of  Jupiter  and  Saturn, 
indicate  that  it  is  a  law  of  the  solar  system  that  the 
smaller  bodies  revolve  about  the  larger.     Thirdly,  on 
the  supposition  that  the  earth  performs  an  annual  revolu 
tion  around  the  sun,  it  is  embraced  along  with  the  plan- 
ets, in  Kepler's  law,  that  the  squares  of  the  times  are  as 
the  cubes  of  the  distances ;  otherwise,  it  forms  an  ex- 
ception, and  the  only  known  exception  to  this  law. 

340.  It  only  remains  to  inquire,  whether  there  sub- 
sist higher  orders  of  relations  between  the  stars  them- 
selves. 


339.  State  the  three  reasons  why  the  planets  revolve  about 
the  sun — how  argued  from  the  phases  of  Mercury  and  Venus  1 
from  the  aspects  and  positions  of  the  superior  planets  ?  from 
the  annual  motion  of  the  earth  ? 


THE    COPBRNICAN    SYSTEM.  275 

The  revolutions  of  the  binary  stars  afford  conclusive 
evidence  of  at  least  subordinate  systems  of  suns,  gov- 
erned by  the  same  laws  as  those  which  regulate  the  mo- 
tions of  the  solar  system.  The  nebulce  also  compose 
peculiar  systems,  in  which  the  members  are  evidently 
bound  together  by  some  common  relation. 

In  these  marks  of  organization, — of  stars  associated 
together  in  clusters, — of  sun  revolving  around  sun, — 
and  of  nebulae  disposed  in  regular  figures,  we  recognize 
different  members  of  some  grand  system,  links  in  one 
great  chain  that  binds  together  all  parts  of  the  universe  ; 
as  we  see  Jupiter  and  his  satellites  combined  in  one  sub- 
ordinate system,  and  Saturn  and  his  satellites  in  another, 
— each  a  vast  kingdom,  and  both  uniting  with  a  num- 
ber of  other  individual  parts  to  compose  an  empire  still 
more  vast. 

341.  This  fact  being  now  established,  that  the  stars 
are  immense  bodies  like  the  sun,  and  that  they  are  sub- 
ject to  the  laws  of  gravitation,  we  cannot  conceive  how 
they  can  be  preserved  from  falling  into  final  disorder  and 
ruin,  unless  they  move  in  harmonious  concert  like  the 
members  of  the  solar  system.  Otherwise,  those  that 
are  situated  on  the  confines  of  creation,  being  retained 
by  no  forces  from  without,  while  they  are  subject  to  the 
attraction  of  all  the  bodies  within,  must  leave  their  sta- 
tions, and  move  inward  with  accelerated  velocity,  and 
thus  all  the  bodies  in  the  universe  would  at  length  fall 
together  in  the  common  center  of  gravity.  The  im- 
mense distance  at  which  the  stars  are  placed  from  each 
other,  would  indeed  delay  such  a  catastrophe  ;  but  such 
must  be  the  ultimate  tendency  of  the  material  world,  un- 


340.  Proofs  of  higher  orders  of  relations  among  the  stars 
themselves — from  the  binary  stars — from  the  nebulae.     What 
do  we  recognize  in  these  marks  of  organization  ? 

341.  How  are  these  systems  preserved  from  falling  into  dis- 
order and  ruin  ?     How  should  we  be  justified  in  inferring  that 
other  worlds  are  not  subject  to  forces  which  operate  to  hasten 
their  decay?     To  what  final  conclusions  are  we  led? 


276  SYSTEM   OF   THE    WORLD. 

less  sustained  in  one  harmonious  system  by  nicely  ad- 
justed motions.  To  leave  entirely  out  of  view  our  con- 
fidence in  the  wisdom  and  preserving  goodness  of  the 
Creator,  and  reasoning  merely  from  what  we  know  of 
the  stability  of  the  solar  system,  we  should  be  justified 
in  inferring,  that  other  worlds  are  not  subject  to  forces 
which  operate  only  to  hasten  their  decay,  and  to  involve 
them  in  final  ruin. 

We  conclude,  therefore,  that  the  material  universe  is 
one  great  system ;  that  the  combination  of  planets  with 
their  satellites  constitutes  the  first  or  lowest  order  of 
worlds ;  that  next  to  these  planets  are  linked  to  suns ; 
that  these  are  bound  to  other  suns,  composing  %  a  still 
higher  order  in  the  scale  of  being ;  and,  finally,  that  all 
the  different  systems  of  worlds,  move  around  their  com- 
mon center  of  gravity. 


SUPPLEMENT, 


CONTAINING  AN  ACCOUNT  OF  THE  LATES1  DISCOV- 
ERIES IN  ASTRONOMY. 


Art.  I.  GREAT  COMET  OF  1843.— On  the  28th  of  Feb- 
ruary, 1843,  the  attention  of  numerous  observers,  in 
various  parts  of  the  world,  was  arrested  by  a  comet 
seen  at  noonday  a  little  eastward  of  the  sun.  It  re- 
sembled a  white  cloud  of  great  density,  being  nearly 
equally  brilliant  through  its  whole  length,  which  at 
this  time  was  estimated  by  different  observers  to  be 
about  three  degrees.  During  the  first  week  in  March, 
the  appearance  of  the  comet  in  the  southern  hemi- 
sphere was  splendid  and  magnificent,  enhanced,  in 
both  respects,  by  the  transparency  of  a  tropical  sky, 
and  the  higher  angle  of  elevation  above  that  at  which 
it  was  seen  by  northern  observers.  At  Pernambuco, 
in  South  America,  on  the  4th  of  March,  it  presented  a 
golden  hue ;  and  it  was,  as  described  by  the  com- 
mander of  a  ship,  so  brilliant  as  to  throw  a  strong 
light  on  the  sea. 

At  New  Haven,  the  comet  was  first  seen  after  sun- 
set on  the  5th  of  March,  and  by  the  writer  on  the  6th. 
It  then  lay  far  in  the  southwest.  On  account  of  the 
presence  of  the  moon,  it  was  not  seen  under  the  most 
favorable  circumstances  until  the  evening  of  the  17th. 
It  then  stretched  along  the  southern  sky  from  the  point 
of  sunset  to  the  bright  star  Sirius,  covering  a  space 
40  deg.  in  length,  but  unusually  limited  in  breadth, 
the  whole  figure  resembling  that  of  a  long  goose-quill, 
being  similarly  curved.  It  was,  at  first,  of  a  delicate 
rose-red  color,  but  afterwards  nearly  a  pure  white. 


278  DISTANCES  OF  THE  STARS. 

All  the  astronomers  of  the  age  have  concurred  in 
the  opinion,  that  this  is  one  of  the  most  remarkable 
exhibitions  of  a  comet  ever  witnessed,  although  they 
are  not  fully  agreed  respecting  the  elements  of  its 
orbit,  or  its  periodic  time.  Some  maintain  that  its 
time  of  revolution  is  175  years,  and  consequently  that 
the  present  is  its  first  return  since  1668;  but  others 
think  that  its  true  period  is  21  f  years,  and  that  it  will 
visit  our  sphere  again  in  1865.  It  passed  its  perihelion 
on  the  27th  of  February,  at  which  time  it  almost 
grazed  the  surface  of  the  sun,  approaching  nearer  to 
that  luminary  than  any  comet  hitherto  observed.  Its 
motions  at  this  time  were  astonishingly  swift,  and  its 
brilliancy  such  as  to  induce  the  belief  that  it  was  at  a 
white  heat  through  its  whole  extent. 

Art  II.  DISTANCES  OP  THE  STARS. — After  many  fruit- 
less and  delusory  efforts  to  measure  the  immense  in- 
terval that  separates  us  from  the  fixed  stars,  the  great 
Prussian  astronomer,  Bessel,  in  the  year  1838,  deter- 
mined this  interesting  and  important  element  by  ob- 
servations on  a  double  star  in  the  Swan,  (61  Cygni.) 

By  observations  of  the  last  degree  of  refinement, 
conducted  for  a  period  of  several  years,  a  parallax 
(see  page  36)  was  decisively  indicated  amounting  to 
about  one  third  of  a  second;  or,  more  exactly,  to 
0".3483,  implying  a  distance  of  592,200  times  the 
mean  distance  of  the  earth  from  the  sun ;  or  a  space 
which  it  would  take  light,  moving  at  the  rate  of 
twelve  millions  of  miles  per  minute,  9£  years  to  tra- 
verse. To  form  some  familiar  notions  of  this  distance, 
let  us  suppose  a  railway-car  to  travel  night  and  day 
at  the  rate  of  twenty  miles  an  hour,  we  should  find  it 
would  take  it  about  547  years  to  reach  the  sun ;  but 
to  reach  61  Cygni  would  require  324,000,000  of  years. 

The  observations  of  Bessel  enabled  him  to  estimate 
also  the  period  of  revolution  of  the  two  stars  compo- 
sing the  Binary  System  (see  p.  255)  of  61  Cygni,  and 
the  dimensions  of  the  orbit ;  and  he  found  the  period 


NEW  PLANETS.  279 

about  540  years,  and  the  length  of  the  orbit  about  2| 
times  that  of  Uranus.  Knowing  also  the  distance  of 
this  star,  we  can  now  determine,  from  its  proper  mo- 
tion (five  seconds  a  year)  the  velocity  with  which  it 
moves  :  this  is  found  to  be  forty-four  miles  per  second, 
— more  than  double  that  of  the  earth  in  its  orbit — 
amounting  to  about  one  "thousand  millions  of  miles 
per  annum. 

On  account  of  the  smallness  of  the  supposed  paral- 
lax thus  found,  it  would  not  be  unreasonable  still  to 
entertain  a  lingering  suspicion,  that  it  is  nothing  more 
than  the  unavoidable  imperfection  of  instrumental 
measurements;  but  the  most  satisfactory  evidence 
which  the  world  can  have  that  such  is  not  the  fact 
in  the  present  instance,  but  that  the  parallax  is  truly 
found,  is  that  the  most  celebrated  astronomers  of  the 
age,  after  rigorous  scrutiny,  have  acknowledged  the 
reality  and  soundness  of  the  determination. 

Several  other  stars  have  of  late  been  supposed  to 
indicate  a'parallax ;  and  one  of  them,  (Alpha  Centauri,) 
the  brightest  star  of  the  Centaur,  a  constellation  of  the 
southern  hemisphere,  is  thought  by  some  to  be  nearer 
to  us  than  61  Cygni,  having  a  parallax  of  nine-tenths 
of  a  second,  The  evidence,  however,  upon  which  this 
case  and  several  similar  cases  of  supposed  parallax 
rest,  is  not  such  as  to  have  inspired  so  high  a  degree 
of  confidence  as  the  determination  by  Bessel,  and  it  is 
still  claimed  only  that  the  distance  of  one  star,  namely, 
61  Cygni,  is  accurately  measured. 

Art.  III.  NEW  PLANETS. — The  discovery  of  the  planet 
Neptune  by  a  distinguished  French  astronomer,  Le 
Verrier,  is  one  of  the  most  remarkable  events  in  as- 
tronomy ;  both  its  existence  and  its  place  in  the  heav- 
ens having  been  determined  by  mathematical  calcula- 
tion, founded  on  the  doctrine  of  universal  gravitation, 
before  it  was  seen  by  the  telescope.  The  method  of 
investigation,  although  laborious  and  intricate,  is  not 
difficult  to  be  understood,  and  may  be  explained  in 


280  NEW  PLANETS. 

very  simple  terms.  The  planet  Uranus  has  long  been 
known  to  be  subject  to  certain  irregularities  in  its 
revolution  around  the  sun,  not  accounted  for  by  all 
the  known  causes  of  perturbation.  In  some  cases, 
the  deviation  from  the  true  place,  as  given  by  the 
latter,  differs  from  actual  observation  two  minutes  of 
a  degree, — a  quantity,  indeed,  which  seems  small,  but 
which  is  still  far  greater  than  occurs  in  the  case  of  the 
other  planets,  Jupiter  and  Saturn  for  example,  and  far 
too  great  to  satisfy  the  extreme  accuracy  required  by 
modern  astronomy.  This  long  since  suggested  to  as- 
tronomers the  possibility  of  one  or  more  additional 
planets,  hitherto  undiscovered,  which,  by  their  attrac- 
tions, exerted  on  Uranus  a  great  disturbing  influence. 
Le  Verrier,  assuming  the  existence  of  such  a  planet, 
applied  himself,  by  the  aid  of  the  most  profound  math- 
ematical calculations  guided  by  the  law  of  gravitation, 
to  the  inquiry  :  Where  is  it  situated — at  what  distance 
from  the  sun — and  in  what  point  of  the  starry  heavens  ? 
As  Saturn  is  nearly  twice  as  far  from  the  sun  as  Ju- 
piter, and  Uranus  just  twice  as  far  as  Saturn,  he  in- 
ferred that,  if  a  planet  exists  beyond  Uranus,  its  dis- 
tance is  probably  twice  that  of  Uranus,  or  about  thirty- 
six  millions  of  miles  from  the  sun.  After  reasoning 
from  analogy,  and  the  doctrine  of  universal  gravita- 
tion, respecting  the  position  and  quantity  of  matter 
which  a  body  must  have  in  order  to  occasion  the  per- 
turbations of  Uranus  to  be  accounted  for,  and  sub- 
mitting the  whole  to  mathematical  calculation,  he  was 
enabled  to  say  that  the  planet  was  just  then  passing 
its  opposition,  and  was  consequently  most  favorably 
situated  for  observation,  and,  on  account  of  the  slow- 
ness of  its  motion,  would  remain  in  a  very  favorable 
position  for  three  months  afterwards.  Le  Verrier 
wrote  to  M.  Galle,  a  practical  astronomer  of  Berlin, 
communicating  his  latest  results,  and  requesting  him 
to  reconnoitre  for  the  stranger,  directing  his  telescope 
to  a  point  about  five  degrees  eastward  of  the  well- 
known  star  Delta  Capricorni.  That  astronomer  no 


NEW  PLANETS.  281 

sooner  pointed  his  telescope  to  the  region  assigned, 
than  he  at  once  recognised  the  body,  its  place  being 
only  52  minutes  of  a  degree  distant  from  thje  position 
marked  out  for  it  by  Le  Verrier,  and  its  apparent  di- 
ameter being  almost  the  same  that  he  had  assigned. 

By  a  singular  coincidence,  a  young  mathematician 
of  the  University  of  Cambridge,  (Eng.,)  Mr.  Adams, 
had,  without  the  least  knowledge  of  what  M.  Le  Ver- 
rier was  doing,  arrived  at  the  same  great  result.  But 
having  failed  to  publish  his  paper  until  the  world  was 
made  acquainted  with  the  facts  through  the  other 
medium,  he  has  lost  much  of  the  honor  which  the 
priority  of  the  discovery  would  have  gained  for  him. 
Thus  two  distinguished  mathematicians,  unknown  to 
each  other,  and  by  entirely  independent  processes,  ar- 
rived at  the  same  results,  as  regarded  both  the  exist- 
ence of  the  supposed  planet,  and  the  region  of  the 
starry  heavens  where  at  that  time  it  lay  concealed ; 
and,  to  crown  all,  astronomers,  in  obedience  to  the 
directions  of  one  of  them,  pointed  their  telescopes  to 
the  spot,  and  found  it  there.  The  conviction  on  the 
mind  of  every  one  was,  that  nothing  but  absolute  truth 
could  abide  a  test  so  unequivocal. 

This  is  justly  regarded  as  one  of  the  greatest  results 
ever  reached  by  pure  mathematical  reasoning;  and 
nothing  could  better  convince  us  of  the  power  of  the 
Calculus,  (the  highest  branch  of  mathematical  science,) 
as  an  instrument  for  guiding  human  thought  in  the 
investigation  of  truth,  than  its  pointing  out  the  place 
of  a  body,  which  had  lain  concealed  in  the  starry  fir- 
mament from  the  creation  of  the  world  to  the  present 
time,  and  which  is  so  small  as  to  be  visible  only  to  a 
large  telescope.  It  is  like  finding  a  single  pearl  buried 
in  the  depths  of  the  ocean,  or  a  grain  of  gold  hidden 
among  the  sands  of  the  seashore.  Nor  has  any  dis- 
covery ever  more  fully  illustrated  the  immutability  of 
truth,  and  its  fertility,  or  that  property  by  which  the 
discovery  of  one  great  truth  conducts  the  human  mind 
to  others  which  before  lay  entirely  beyond  its  reaoh. 


282  CENTER  OF  THE  UNIVERSE. 

This,  as  well  as  many  other  great  truths  hidden  in  the 
abysses  of  the  universe,  is  among  the  legitimate  fruits 
of  Newton's  grand  discovery — the  law  of  Universal 
Gravitation.  ^. 

One  satellite  accompanying  Neptune  has  already 
been  discovered,  and  the  existence  of  another  satellite, 
and  of  a  ring  resembling  that  of  Saturn,  is  strongly 
suspected,  but  is  not  fully  confirmed. 

Asteroids.  In  addition  to  the  four  small  planets, 
Ceres,  Pallas,  Juno,  and  Vesta,  discovered  near  the 
beginning  of  the  present  century,  and  having  their 
orbits  in  the  long  space  between  Mars  and  Jupiter, 
five  more  similar  bodies  have  recently  been  revealed 
to  us,  lying  in  the  same  region  of  the  heavens,  namely 
— Astrcea,  Iris,  Hebe,  Flora,  and  Metis.  Like  the  former, 
they  are  very  small  bodies,  as  faint  stars  visible  only 
to  the  telescope,  and  are  characterized  by  orbits  of 
greater  eccentricity  than  those  of  the  old  planets. 
This  multiplication  of  asteroids  faintly  countenances 
the  hypothesis  of  Dr.  Olbers,  one  of  the  original  dis- 
coverers of  this  class  of  bodies, — that  "  they  are  frag- 
ments of  a  single  large  planet  that  once  occupied  the 
same  region  between  Mars  and  Jupiter." 

Art.  IV.  CENTER  OF  THE  UNIVERSE. — At  the  end  of  the 
preceding  work,  we  have  suggested  reasons  for  be- 
lieving that  the  whole  host  of  heaven  revolve  around 
a  common  center.  Dr.  Maedler,  of  the  Imperial  Ob- 
servatory at  Dorpat,  has  recently  not  only  asserted 
this  doctrine,  but  has  endeavored  to  show  the  exact 
position  of  that  center.  He  fixes  it  jn  the  Pleiades, 
and  asserts  that  Alcyone,  the  brightest  star  of  this 
group,  is  the  true  "  central  sun,"  around  which  all  the 
stars  of  our  visible  firmament  revolve,  in  obedience  to 
the  law  of  universal  gravitation.  The  proofs  of  this 
remarkable  hypothesis  are  deemed  too  incomplete,  at 
present,  to  command  entire  assent ;  but  the  method  of 
investigation  pursued  by  this  distinguished  astrono- 
mer, opens  a  new  field  of  observation  and  of  specula- 


TELESCOPES.  283 

tion,  and  promises  to  lend  a  new  interest  to  inquirers 
into  the  mechanism  of  the  heavens. 

Art.  V.  TELESCOPES. — Practical  Astronomy  has  of 
late  been  enriched  with  a  number  of  great  telescopes, 
which  have  discovered  new  wonders  in  the  starry 
heavens.  The  most  remarkable  of  these  are  the  grand 
Reflector  constructed  by  Lord  Rosse,  an  Irish  noble- 
man, and  the  great  Refractors  belonging  respectively 
to  the  Pulkova,  the  Cincinnati,  and  the  Cambridge 
observatories. 

Lord  Rosse's  telescope  considerably  exceeds  in  di- 
mensions the  great  40  feet  reflector  of  Sir  William 
Herschel,  being  50  feet  in  focal  length,  and  having  a 
diameter  of  6  feet ;  whereas  that  of  the  Herschelian 
telescope  was  only  4  feet.  This  unexampled  magni- 
tude makes  this  instrument  superior  to  all  others  in 
light,  and  fits  it  pre-eminently  for  observations  on  the 
most  remote  and  obscure  celestial  objects,  as  the  faint- 
est nebulae,  for  example.  But  its  unwieldy  size,  and 
its  liability  to  loss  of  power  by  the  tarnishing  or  tem- 
porary blurring  of  the  great  speculum,  will  render  it 
far  less  available  for  actual  research  than  the  great 
refractors  which  come  in  competition  with  it. 

Until  recently,  it  was  thought  impossible  to  form 
achromatic  object-glasses  for  telescopes  of  more  than 
about  five  inches  diameter ;  but  they  have  been  suc- 
cessively enlarged,  until  we  can  no  longer  set  bounds 
to  the  dimensions  which  they  may  finally  assume. 
The  Pulkova  telescope  (at  St.  Petersburg)  has  a  clear 
aperture  of  about  15  inches  and  a  focal  length  of  22 
feet.  That  of  Cincinnati  is  somewhat  smaller,  its  ob- 
ject-glass being  12  inches  in  diameter,  and  its  length 
17  feet.  The  telescope  recently  acquired  by  Harvard 
University,  is  perhaps  the  finest  refractor  hitherto 
constructed.  Its  dimensions  are  nearly  the  same  with 
those  of  the  Pulkova  instrument,  but  its  performances 
are  thought  to  be  superior  even  to  that.  It  has  recently 
added  to  the  system  of  Saturn  an  eighth  satellite. 


284  TELESCOPES. 

These  magnificent  telescopes  have  afforded  views 
of  celestial  'objects,  more  splendid  and  exciting  than 
any  previously  enjoyed  by  man.  In  a  scientific  point 
of  view,  the  most  interesting  of  these  revelations  con- 
sist in  the  resolution  of  Nebulae  before  deemed  irre- 
solvable, and  thus  countenancing  the  idea  that  this 
term  is  applicable  only  to  the  comparative  powers  of 
our  instruments ;  that,  if  any  objects  of  this  class  re- 
main unresolved,  it  will  only  be  because  the  telescope 
has  not  yet  acquired  the  requisite  power  to  separate 
them  into  stars.  Under  these  mighty  instruments, 
what  was  before  a  faint  wisp  of  fog  on  the  confines 
of  creation,  expands  suddenly  into  innumerable  suns, 
composing  a  glorious  firmament  of  stars.  The  Cam- 
bridge telescope  has  succeeded  in  the  resolution  of  the 
great  Nebula  of  Orion,  more  complete  than  had  been 
effected  even  by  Lord  Rosse's  "  Leviathan  Reflector," 
and  is  thus  proved  to  be  one  of  the  finest  instruments 
(probably  the  finest  refractor)  in  the  world. 


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925 


MAY  21  196815 


MAY   8  '68  ^2  AW 


DEPT. 


U.  C.  BERKELEY  LIBRARIES 


